Updated: April 11th, 2023 10:13

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

Source: Web Of Science

Added: June 13, 2022

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

Sources: Web Of Science, ORCID

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

Sources: ORCID, Web Of Science

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

Sources: Web Of Science, ORCID

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

Sources: ORCID, Web Of Science

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.

Sources: Web Of Science, ORCID

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.

author keywords: optimization; optimization under uncertainty; spatiotemporal fractionation; treatment planning

Sources: Web Of Science, ORCID

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

Sources: Web Of Science, ORCID

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

Sources: Web Of Science, ORCID

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, ORCID

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2017 journal article

Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy

*Radiotherapy and Oncology*, *125*(2), 357–364.

author keywords: Liver SBRT; Dose escalation; Fractionation; Treatment plan optimization

Sources: Crossref, ORCID

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

Sources: Web Of Science, ORCID

Added: August 6, 2018

2016 journal article

Technical Note: Improving the VMERGE treatment planning algorithm for rotational radiotherapy

*MEDICAL PHYSICS*, *43*(7), 4093–4097.

author keywords: arc therapy; treatment planning; optimization; rotational therapy

Sources: Web Of Science, ORCID

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

Sources: Web Of Science, ORCID

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

Sources: Web Of Science, ORCID

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.

author keywords: Scenario generation; Stochastic optimization; Discretization; Sparse grid

Sources: Web Of Science, ORCID

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)

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: Crossref, ORCID

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

Sources: ORCID, Crossref

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

Sources: Crossref, ORCID

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

Added: July 28, 2019

Updated: August 14th, 2019 08:11

2005 - 2011