An inexact primal-dual algorithm for semi-infinite programming

Bo Wei (), William B. Haskell () and Sixiang Zhao ()
Additional contact information
Bo Wei: National University of Singapore
William B. Haskell: Purdue University
Sixiang Zhao: Shanghai Jiao Tong University

Mathematical Methods of Operations Research, 2020, vol. 91, issue 3, No 5, 544 pages

Abstract: Abstract This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. We create a new prox function for nonnegative measures for the dual update, and it turns out to be a generalization of the Kullback-Leibler divergence. We show that, with a tolerance for small errors (approximation and regularization error), this algorithm achieves an $${\mathcal {O}}(1/\sqrt{K})$$O(1/K) rate of convergence in terms of the optimality gap and constraint violation, where K is the total number of iterations. We then use our general error bounds to analyze the convergence and sample complexity of a specific primal-dual SIP algorithm based on Monte Carlo sampling. Finally, we provide numerical experiments to demonstrate the performance of this algorithm.

Keywords: Semi-infinite programming; Primal-dual algorithms; Monte Carlo integration (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-019-00698-2

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