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)

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.

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).

Contributors: J. Tóth ^{*}, A. Nagy ^{*} & ^{ n}

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.

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.

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

Updated: August 14th, 2019 08:11

2005 - 2011

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