A note on generalized semi-infinite program bounding methods

2019/12/02 by Harwood, Stuart M.
#90C34 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1912.01075

Abstract

Generalized semi-infinite programs (GSIP) are a class of mathematical optimization problems that generalize semi-infinite programs, which have a finite number of decision variables and infinite constraints. Mitsos et al. (Mitsos and Tsoukalas. "Global optimization of generalized semi-infinite programs via restriction of the right hand side." Journal of Global Optimization 61.1 (2015): 1-17.) present a method for global optimization of GSIP. This method involves a lower bounding method, and they claim that these lower bounds converge to the optimal objective value of the GSIP. A counterexample is presented that shows that this claim is false.

Related

• Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs
• Bounding-Focused Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs
• A global approach for generalized semi-infinte programs with polyhedral parameter sets
• Constraint Qualifications and Optimality Conditions for Nonconvex Semi-Infinite and Infinite Programs
• Outer-space branch-and-bound algorithm for generalized linear multiplicative programs