Collaborative Research: Further Developments in the Global Resolution of Convex Programs with Complementary Contraints
Final rept. 1 Sep 2011-31 Aug 2014
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES
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We have developed methods for finding globally optimal solutions to various classes of nonconvex optimization problems. We have shown that any nonconvex conic quadratically constrained quadratic program can be lifted to a convex conic optimization problem. We have shown that a complementarity approach can be used to find sparse solutions to optimization problems, with promising initial theoretical and computational results. We have investigated various relaxation approaches to several classes of problems with complementarity constraints, including linear programs with complementarity constraints, support vector regression parameter selection, bi-parametric linear complementarity constrained linear programs, quadratic programs with complementarity constraints, and nonconvex quadratically constrained quadratic programs, proving various theoretical results for each of these problems as well as demonstrating the computational effectiveness of our approaches.
- Operations Research