Near-optimal solutions of convex semi-infinite programs via targeted sampling

Souvik Das (), Ashwin Aravind (), Ashish Cherukuri () and Debasish Chatterjee ()
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Souvik Das: Indian Institute of Technology Bombay
Ashwin Aravind: Indian Institute of Technology Bombay
Ashish Cherukuri: University of Groningen
Debasish Chatterjee: Indian Institute of Technology Bombay

Annals of Operations Research, 2022, vol. 318, issue 1, No 5, 129-146

Abstract: Abstract We propose an approach to find the optimal value of a convex semi-infinite program (SIP) that involves identifying a finite set of relevant constraints by solving a finite-dimensional global maximization problem. One of the major advantages of our approach is that it admits a plug-and-play module where any suitable global optimization algorithm can be employed to obtain the optimal value of the SIP. As an example, we propose a simulated annealing based algorithm which is useful especially when the constraint index set is high-dimensional. A proof of convergence of the algorithm is included, and the performance and accuracy of the algorithm itself are illustrated on several benchmark SIPs lifted from the literature.

Keywords: Semi-infinite programming; Targeted sampling; Convexity; Global optimization; 46N10; 65K10; 65C05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-022-04810-4

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