Works (44)
Updated: April 4th, 2024 16:16
2024 journal article
Rational dual certificates for weighted sums-of-squares polynomials with boundable bit size
JOURNAL OF SYMBOLIC COMPUTATION, 121.
author keywords: Polynomial optimization; Nonnegativity certificates; Sums-of-squares decomposition; Computational real algebraic geometry; Conic programming
TL;DR:
This article analyzes the complexity of rational dual certificates of WSOS polynomials by bounding the bit sizes of integer dual certificates as a function of parameters such as the degree and the number of variables of the polynmials, or their distance from the boundary of the cone.
(via Semantic Scholar)
arxiv.org (repository)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: January 2, 2024
2023 journal article
Duality of sum of nonnegative circuit polynomials and optimal SONC bounds
JOURNAL OF SYMBOLIC COMPUTATION, 114, 246–266.
author keywords: Polynomial optimization; Nonnegativity certificates; Circuit polynomials; Convex optimization; Duality; Power cone
TL;DR:
The proof, based on convex programming duality, removes the nondegeneracy assumption and motivates an algorithm that generates an optimal set of circuits and computes the corresponding SONC bound in a manner that is particularly attractive for sparse polynomials.
(via Semantic Scholar)
Source: Web Of Science
Added: June 13, 2022
2023 article
Spatiotemporal fractionation schemes for stereotactic radiosurgery of multiple brain metastases
Torelli, N., Papp, D., & Unkelbach, J. (2023, June 15). MEDICAL PHYSICS, Vol. 6.
author keywords: fractionation; multiple brain metastases; stereotactic radiosurgery; treatment plan optimization
TL;DR:
Although cSTF cannot achieve the full BED reduction of STF, it improves on uniform fractionation and is more robust against both setup errors and biological uncertainties related to partial tumor irradiation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: July 3, 2023
2023 journal article
The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 310(2), 511–517.
author keywords: Semidefinite optimization; Static equilibrium; Monostatic polyhedron; Polynomial inequalities
Sources: Web Of Science, NC State University Libraries, ORCID
Added: July 10, 2023
2022 journal article
A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments
PHYSICS IN MEDICINE AND BIOLOGY, 67(18).
author keywords: combined proton-photon radiotherapy; IMRT; IMPT; stochastic optimization
MeSH headings : Humans; Neoplasms / radiotherapy; Organs at Risk; Photons / therapeutic use; Proton Therapy / methods; Protons; Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods
TL;DR:
A novel stochastic optimization method is developed to directly incorporate range and setup errors into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans for safe clinical implementation of optimized proton–photon radiotherapy.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: September 19, 2022
2022 journal article
DUAL CERTIFICATES AND EFFICIENT RATIONAL SUM-OF-SQUARES DECOMPOSITIONS FOR POLYNOMIAL OPTIMIZATION OVER COMPACT SETS
SIAM JOURNAL ON OPTIMIZATION, 32(4), 2461–2492.
author keywords: Key words; polynomial optimization; nonnegativity certificates; sum-of-squares; nonsymmetric conic optimization
TL;DR:
The concept of dual cone certificates is introduced, which allows us to interpret vectors from the dual of the sum-of-squares cone as rigorous nonnegativity certificates of a WSOS polynomial.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: October 5, 2022
2022 article
Technical note: Optimal allocation of limited proton therapy resources using model-based patient selection
Papp, D., & Unkelbach, J. (2022, June 26). MEDICAL PHYSICS, Vol. 6.
author keywords: Markov decision process; patient selection; proton therapy
MeSH headings : Humans; Patient Selection; Photons / adverse effects; Probability; Proton Therapy / methods; Protons; Radiotherapy Planning, Computer-Assisted / methods
TL;DR:
The goal is to determine the ΔNTCP thresholds for selecting a patient for proton therapy, which optimally balance the competing goals of making use of all available slots while not blocking slots with patients with low benefit.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: July 5, 2022
2021 article
Alfonso: Matlab Package for Nonsymmetric Conic Optimization
Papp, D., & Yildiz, S. (2021, September 8). INFORMS JOURNAL ON COMPUTING, Vol. 34.
author keywords: conic optimization; interior-point method; self-concordant barrier; nonsymmetric cone; software
TL;DR:
Alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones, enables optimization over any convex cone as long as a logarithmically homogeneous self-concordant barrier is available for the cone or its dual.
(via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: September 9, 2021
2021 journal article
Optimal Allocation of Proton Therapy Slots in Combined Proton-Photon Radiation Therapy
INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS, 111(1), 196–207.
MeSH headings : Deglutition Disorders / etiology; Head and Neck Neoplasms / radiotherapy; Humans; Photons / therapeutic use; Proton Therapy / adverse effects; Proton Therapy / methods; Radiotherapy, Intensity-Modulated / adverse effects; Xerostomia / etiology
TL;DR:
Combined proton-photon treatments with flexible proton slot assignment provide a method to make optimal use of all available resources and allow for a better utilization of limited proton therapy resources.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: November 8, 2021
2021 article
alfonso: Matlab package for nonsymmetric conic optimization
(2021, January 12).
Source: ORCID
Added: January 23, 2021
2019 article
Duality of sum of nonnegative circuit polynomials and optimal SONC bounds
(2019, December 10).
Source: ORCID
Added: January 23, 2021
2019 journal article
Robust spatiotemporal fractionation schemes in the presence of patient setup uncertainty
MEDICAL PHYSICS, 46(7), 2988–3000.
Contributors: M. Gaddy n, J. Unkelbach* & n
author keywords: optimization; optimization under uncertainty; spatiotemporal fractionation; treatment planning
MeSH headings : Dose Fractionation, Radiation; Humans; Liver Neoplasms / radiotherapy; Models, Statistical; Probability; Proton Therapy; Radiotherapy Planning, Computer-Assisted / methods; Stochastic Processes; Uncertainty
TL;DR:
In the presence of patient setup uncertainty, spatiotemporally fractionated treatment plans exhibit the same robust tumor coverage as their uniformly fractionated counterparts and still retain the benefit in sparing healthy tissues.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 5, 2019
2019 journal article
SUM-OF-SQUARES OPTIMIZATION WITHOUT SEMIDEFINITE PROGRAMMING
SIAM JOURNAL ON OPTIMIZATION, 29(1), 822–851.
author keywords: sum-of-squares optimization; nonsymmetric conic optimization; polynomial interpolation; polynomial optimization; semidefinite programming
TL;DR:
A homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation, which has substantially lower theoretical time and space complexity than the conventional SDP-based approach.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: April 9, 2019
2019 journal article
Semi-Infinite Programming
Wiley StatsRef: Statistics Reference Online.
Source: ORCID
Added: August 15, 2019
2018 journal article
Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit
PHYSICS IN MEDICINE AND BIOLOGY, 63(1).
author keywords: treatment planning; optimization; spatiotemporal fractionation
MeSH headings : Dose Fractionation, Radiation; Humans; Liver Neoplasms / radiotherapy; Organs at Risk / radiation effects; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy Planning, Computer-Assisted / standards; Radiotherapy, Intensity-Modulated / methods; Treatment Outcome
TL;DR:
The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potentialnormal tissue dose reduction.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
PO-0900: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
Radiotherapy and Oncology, 127, S479–S480.
Sources: Crossref, NC State University Libraries
Added: January 25, 2020
2018 book
Reaction kinetics: Exercises, programs and theorems: Mathematica for deterministic and stochastic kinetics
In Reaction Kinetics: Exercises, Programs and Theorems: Mathematica for Deterministic and Stochastic Kinetics (pp. 1–469).
Source: ORCID
Added: August 12, 2019
2017 journal article
SEMI-INFINITE PROGRAMMING USING HIGH-DEGREE POLYNOMIAL INTERPOLANTS AND SEMIDEFINITE PROGRAMMING
SIAM JOURNAL ON OPTIMIZATION, 27(3), 1858–1879.
author keywords: sum-of-squares; interpolation; polynomial optimization; semi-infinite programming; design of experiments; semidefinite optimization
TL;DR:
The proposed reformulations are sufficiently well scaled that they can be solved easily with every commonly used semidefinite programming solver, such as SeDuMi, SDPT3, and CSDP.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2017 journal article
Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
Radiotherapy and Oncology, 125(2), 357–364.
Contributors: J. Unkelbach *, n , M. Gaddy n, N. Andratschke *, T. Hong * & M. Guckenberger *
author keywords: Liver SBRT; Dose escalation; Fractionation; Treatment plan optimization
MeSH headings : Dose Fractionation, Radiation; Humans; Liver Neoplasms / diagnostic imaging; Liver Neoplasms / radiotherapy; Radiosurgery / methods; Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods
TL;DR:
Spatiotemporal fractionation may reduce the risk of liver toxicity or facilitate dose escalation in liver SBRT in circumstances where the mean dose to the non-involved liver is the prescription-limiting factor.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2017 conference paper
Univariate polynomial optimization with sum-of-squares interpolants
Springer Proceedings in Mathematics and Statistics, 213, 143–162.
TL;DR:
It is shown that a reformulation of the sum-of-squares SDP using polynomial interpolants yields a substantial improvement over the standard formulation, and problems involving sum- of-Squares interpolants of hundreds of degrees can be handled without difficulty by commonly used semidefinite programming solvers.
(via Semantic Scholar)
Source: ORCID
Added: August 12, 2019
2016 journal article
ON THE COMPLEXITY OF LOCAL SEARCH IN UNCONSTRAINED QUADRATIC BINARY OPTIMIZATION
SIAM JOURNAL ON OPTIMIZATION, 26(2), 1257–1261.
author keywords: local optimization; binary quadratic optimization; exponential complexity
TL;DR:
This work considers the problem of finding a local minimum of a binary quadratic function and shows by an elementary construction that every descending local search algorithm takes exponential time in the worst case.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
Technical Note: Improving the VMERGE treatment planning algorithm for rotational radiotherapy
MEDICAL PHYSICS, 43(7), 4093–4097.
Contributors: M. Gaddy n & n
author keywords: arc therapy; treatment planning; optimization; rotational therapy
MeSH headings : Algorithms; Humans; Male; Prostatic Neoplasms / radiotherapy; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods; Spinal Cord Neoplasms / radiotherapy; Time Factors
TL;DR:
In the authors' computational study they found that both proposed modifications, especially the regularization, yield noticeably improved treatment plans for the same treatment times than what can be obtained using the original VMERGE method.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 article
A modular approach to intensity-modulated arc therapy optimization with noncoplanar trajectories
Papp, D., Bortfeld, T., & Unkelbach, J. (2015, July 7). PHYSICS IN MEDICINE AND BIOLOGY, Vol. 60, pp. 5179–5198.
author keywords: arc therapy (VMAT); optimization; noncoplanar radiotherapy; 4pi; treatment planning
MeSH headings : Algorithms; Glioblastoma / surgery; Humans; Lung Neoplasms / surgery; Radiosurgery / methods; Radiosurgery / standards; Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods; Radiotherapy, Intensity-Modulated / standards
TL;DR:
The approach is demonstrated using two particularly challenging cases, where the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanarVMAT plan.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 review
Optimization approaches to volumetric modulated arc therapy planning
[Review of ]. MEDICAL PHYSICS, 42(3), 1367–1377.
author keywords: radiotherapy; treatment plan optimization; VMAT
MeSH headings : Algorithms; Humans; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated
TL;DR:
Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed, and their advantages and limitations are outlined and recommendations for improvements are discussed.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
Scenario generation for stochastic optimization problems via the sparse grid method
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 62(3), 669–692.
Contributors: M. Chen *, S. Mehrotra * & n
author keywords: Scenario generation; Stochastic optimization; Discretization; Sparse grid
TL;DR:
It is indicated that the sparse grid scenario generation method scales well with the dimension of the distribution—especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model
Medical Physics, 42(5), 2234–2241.
author keywords: intensity-modulated proton therapy (IMPT); nonuniform fractionation; biologically equivalent dose (BED)
MeSH headings : Algorithms; Dose Fractionation, Radiation; Humans; Kidney / radiation effects; Proton Therapy / methods; Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods; Skin / radiation effects; Spinal Neoplasms / radiotherapy; Spinal Neoplasms / secondary
TL;DR:
Methodology for treatment planning with nonuniform fractions and a combinatorial algorithm to initialize the pencil beam intensities are developed and demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2014 journal article
A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization
SIAM Journal on Optimization, 24(4), 1670–1697.
author keywords: semi-infinite programming; robust optimization; distributionally robust optimization; stochastic programming; moment matching; column generation; cutting surface methods; cutting plane methods; moment problem
TL;DR:
A central cutting surface algorithm for general semi-infinite convex optimization problems is presented and used to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2014 journal article
Exploiting tumor shrinkage through temporal optimization of radiotherapy
Physics in Medicine and Biology, 59(12), 3059–3079.
author keywords: temporal optimization; split-course radiotherapy; tumor shrinkage; liver tumors
MeSH headings : Humans; Liver Neoplasms / pathology; Liver Neoplasms / radiotherapy; Models, Biological; Neoplasms / pathology; Neoplasms / radiotherapy; Radiation Tolerance / radiation effects; Radiotherapy / adverse effects; Radiotherapy / methods; Time Factors; Treatment Outcome; Tumor Burden / radiation effects
TL;DR:
The analysis of the tumor model suggests that substantial reduction in normal tissue dose can be achieved by exploiting tumor shrinkage via an optimal design of multi-stage treatments for selected disease sites where substantial tumor regression translates into reduced target volumes.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2014 journal article
Plan averaging for multicriteria navigation of sliding window IMRT and VMAT
Medical Physics, 41(2), 021709.
author keywords: VMAT; sliding window; IMRT; dynamic; dMLC; Pareto
MeSH headings : Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods
TL;DR:
The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of Deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencingStep.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2014 journal article
Shape-Constrained Estimation Using Nonnegative Splines
Journal of Computational and Graphical Statistics, 23(1), 211–231.
author keywords: Bernstein polynomials; Density estimation; Nonnegative polynomials; Regression; Second-order programming; Semi-definite programming; Splines
TL;DR:
A general computational framework that treats nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines, and a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2014 journal article
Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset
GigaScience, 3(1).
author keywords: IMRT; Optimization; Radiation therapy; Beam angle optimization; VMAT; Treatment plan optimization
TL;DR:
An open dataset is presented – the first of its kind – to the radiation oncology community, which will allow researchers to compare methods for optimizing radiation dose delivery.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2013 journal article
Direct leaf trajectory optimization for volumetric modulated arc therapy planning with sliding window delivery
Medical Physics, 41(1), 011701.
author keywords: arc therapy; optimization; sliding window; VMAT
MeSH headings : Algorithms; Humans; Male; Neoplasms / radiotherapy; Radiotherapy Dosage; Radiotherapy Planning, Computer-Assisted / methods; Radiotherapy, Intensity-Modulated / methods
TL;DR:
A novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step is proposed.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2013 journal article
Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming
Annals of Operations Research, 208(1), 291–308.
TL;DR:
A summary of methods based on semidefinite programming for estimating arrival rate of nonhomogeneous Poisson processes from a finite set of observed data and a method which requires only linear constraints are presented.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
2013 journal article
Generating Moment Matching Scenarios Using Optimization Techniques
SIAM Journal on Optimization, 23(2), 963–999.
author keywords: scenario generation; moment matching; cubature; column generation; convex programming; statistical bounds; semi-infinite programming
TL;DR:
An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming because of its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2013 journal article
Semidefinite Characterization of Sum-of-Squares Cones in Algebras
SIAM Journal on Optimization, 23(3), 1398–1423.
author keywords: sum of squares; semidefinite programming; semidefinite representability; nonnegative polynomials; sum-of-squares functional systems
TL;DR:
It is shown that many concrete cones are in fact sum-of-squares cones with respect to some algebra and thus are representable by the cone of positive semidefinite matrices and some well-known Chebyshev systems, when extended to Euclidean Jordan algebras, induce cones that are semidfinite representable.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019
2012 report
Generating nested quadrature formulas for general weight functions with known moments
[Technical report].
Source: NC State University Libraries
Added: July 28, 2019
2012 report
Network interdiction--models, applications, unexplored directions
(RUTCOR Research Report No. 4-2012).
Source: NC State University Libraries
Added: July 10, 2019
2012 journal article
Optimal Designs for Rational Function Regression
Journal of the American Statistical Association, 107(497), 400–411.
author keywords: Experimental design; Positive polynomials; Semidefinite programming
TL;DR:
The proposed method generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor, based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well-established numerical optimization methods.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
2012 journal article
ReactionKinetics—A Mathematica package with applications
Chemical Engineering Science, 83, 12–23.
author keywords: Kinetics; Computational chemistry; Graphs of reactions; Stochastic models; Parameter identification; Decomposition of overall reactions
TL;DR:
Requirements are formulated for a reaction kinetics program package to be useful for an as wide as possible circle of users and they are illustrated with examples using ReactionKinetics, a Mathematica based package currently being developed by the authors.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
2011 journal article
Bilinear optimality constraints for the cone of positive polynomials
Mathematical Programming, 129(1), 5–31.
author keywords: Optimality conditions; Positive polynomials; Complementarity slackness; Bilinearity rank; Bilinear cones
TL;DR:
The bil inearity rank of a cone is defined, which is the number of linearly independent bilinear identities valid for points in C({\mathcal K})}, and is extended to trigonometric and exponential polynomials.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
2011 report
Multivariate arrival rate estimation by sum-of-squares polynomial splines and decomposition
[Technical report].
Source: NC State University Libraries
Added: July 28, 2019
2011 journal article
Scenario decomposition of risk-averse multistage stochastic programming problems
Annals of Operations Research, 200(1), 147–170.
author keywords: Dynamic measures of risk; Duality; Decomposition; Bundle methods
TL;DR:
For a risk-averse multistage stochastic optimization problem with a finite scenario tree, a new scenario decomposition method is introduced and its convergence is proved.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: July 28, 2019
2010 journal article
Acyclic, or totally tight, two-person game forms: Characterization and main properties
Discrete Mathematics, 310(6-7), 1135–1151.
author keywords: Game; Game form; Effectivity function; Improvement cycle; Acyclic; Assignable; Tight; Totally tight; Nash-solvable; Dominance-solvable
TL;DR:
This work characterize totally tight game forms, and derive from this characterization that they are tight, Nash-solvable, dominance- solvable, acyclic, and assignable.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 28, 2019
2005 journal article
Effective solution of linear Diophantine equation systems with an application in chemistry
Journal of Mathematical Chemistry, 39(1), 15–31.
author keywords: decomposition of overall reaction; linear Diophantine equations; linear programming
Sources: ORCID, Crossref, NC State University Libraries
Added: July 28, 2019
Education
Updated: August 14th, 2019 08:11
2005 - 2011
Rutgers University New Brunswick New Brunswick, NJ, US
PhD
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