Piecewise SOS-convex moment optimization and applications via exact semi-definite programs
This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-01-01
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| Series: | EURO Journal on Computational Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S219244062400011X |
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| author | Q.Y. Huang V. Jeyakumar G. Li |
| author_facet | Q.Y. Huang V. Jeyakumar G. Li |
| author_sort | Q.Y. Huang |
| collection | DOAJ |
| description | This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the optimal value and an optimal probability measure of the original moment problem. This is done by establishing an SOS representation for the non-negativity of a piecewise SOS-convex function over a projected spectrahedron. Finally, as an application and a proof-of-concept illustration, the paper presents numerical results for the Newsvendor and revenue maximization problems with higher-order moments by solving their equivalent SDP reformulations. These reformulations promise a flexible and efficient approach to solving these models. The main novelty of the present work in relation to the recent research lies in finding the solution to moment problems, for the first time, with piecewise SOS-convex functions from their numerically tractable exact SDP reformulations. |
| format | Article |
| id | doaj-art-3ae1ef4b19e6445ca39d7ee5ab53bc88 |
| institution | Kabale University |
| issn | 2192-4406 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | EURO Journal on Computational Optimization |
| spelling | doaj-art-3ae1ef4b19e6445ca39d7ee5ab53bc882024-12-14T06:30:54ZengElsevierEURO Journal on Computational Optimization2192-44062024-01-0112100094Piecewise SOS-convex moment optimization and applications via exact semi-definite programsQ.Y. Huang0V. Jeyakumar1G. Li2Corresponding author.; Department of Applied Mathematics, University of New South Wales, Sydney 2052, AustraliaDepartment of Applied Mathematics, University of New South Wales, Sydney 2052, AustraliaDepartment of Applied Mathematics, University of New South Wales, Sydney 2052, AustraliaThis paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the optimal value and an optimal probability measure of the original moment problem. This is done by establishing an SOS representation for the non-negativity of a piecewise SOS-convex function over a projected spectrahedron. Finally, as an application and a proof-of-concept illustration, the paper presents numerical results for the Newsvendor and revenue maximization problems with higher-order moments by solving their equivalent SDP reformulations. These reformulations promise a flexible and efficient approach to solving these models. The main novelty of the present work in relation to the recent research lies in finding the solution to moment problems, for the first time, with piecewise SOS-convex functions from their numerically tractable exact SDP reformulations.http://www.sciencedirect.com/science/article/pii/S219244062400011XMoment optimizationSum-of-squares convex polynomialsPiecewise functionsGeneralized moment problemsSemi-definite programming |
| spellingShingle | Q.Y. Huang V. Jeyakumar G. Li Piecewise SOS-convex moment optimization and applications via exact semi-definite programs EURO Journal on Computational Optimization Moment optimization Sum-of-squares convex polynomials Piecewise functions Generalized moment problems Semi-definite programming |
| title | Piecewise SOS-convex moment optimization and applications via exact semi-definite programs |
| title_full | Piecewise SOS-convex moment optimization and applications via exact semi-definite programs |
| title_fullStr | Piecewise SOS-convex moment optimization and applications via exact semi-definite programs |
| title_full_unstemmed | Piecewise SOS-convex moment optimization and applications via exact semi-definite programs |
| title_short | Piecewise SOS-convex moment optimization and applications via exact semi-definite programs |
| title_sort | piecewise sos convex moment optimization and applications via exact semi definite programs |
| topic | Moment optimization Sum-of-squares convex polynomials Piecewise functions Generalized moment problems Semi-definite programming |
| url | http://www.sciencedirect.com/science/article/pii/S219244062400011X |
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