ParetoImageSDP

ParetoImageSDP: approximations of Pareto curves and images of semialgebraic sets. ParetoImageSDP is a set of libraries using the Yalmip and Gloptipoly toolboxes for MATLAB. It provides functions to compute semidefinite approximations of: 1) Pareto curves implementing the three methods described in: Victor Magron, Didier Henrion and Jean-Bernard Lasserre ”Approximating Pareto curves using semidefinite relaxations” (on the arxiv). 2) Images of semialgebraic sets under polynomial applications implementing the two methods described in Victor Magron, Didier Henrion and Jean-Bernard Lasserre ”Semidefinite approximations of projections and polynomial images of semialgebraic sets” (on Optimization Online).


References in zbMATH (referenced in 13 articles , 2 standard articles )

Showing results 1 to 13 of 13.
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  1. Ahmadi, Amir Ali; El Khadir, Bachir: Time-varying semidefinite programs (2021)
  2. Lasserre, Jean Bernard; Magron, Victor; Marx, Swann; Zahm, Olivier: Minimizing rational functions: a hierarchy of approximations via pushforward measures (2021)
  3. Lee, Jae Hyoung; Sisarat, Nithirat; Jiao, Liguo: Multi-objective convex polynomial optimization and semidefinite programming relaxations (2021)
  4. Guo, Feng; Sun, Xiaoxia: On semi-infinite systems of convex polynomial inequalities and polynomial optimization problems (2020)
  5. Klep, Igor; Nie, Jiawang: A matrix Positivstellensatz with lifting polynomials (2020)
  6. Kim, Do Sang; Phạm, Tiến-Son; Tuyen, Nguyen Van: On the existence of Pareto solutions for polynomial vector optimization problems (2019)
  7. Lasserre, Jean B.: Volume of sublevel sets of homogeneous polynomials (2019)
  8. Magron, Victor; Garoche, Pierre-Loic; Henrion, Didier; Thirioux, Xavier: Semidefinite approximations of reachable sets for discrete-time polynomial systems (2019)
  9. Aßmann, Denis; Liers, Frauke; Stingl, Michael; Vera, Juan C.: Deciding robust feasibility and infeasibility using a set containment approach: an application to stationary passive gas network operations (2018)
  10. Chuong, Thai Doan: Linear matrix inequality conditions and duality for a class of robust multiobjective convex polynomial programs (2018)
  11. Weis, Stephan: Operator systems and convex sets with many normal cones (2018)
  12. Magron, Victor; Henrion, Didier; Lasserre, Jean-Bernard: Semidefinite approximations of projections and polynomial images of semialgebraic sets (2015)
  13. Magron, Victor; Henrion, Didier; Lasserre, Jean-Bernard: Approximating Pareto curves using semidefinite relaxations (2014)