Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems

J. O. Royset () and E. Y. Pee
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J. O. Royset: Naval Postgraduate School
E. Y. Pee: Defence Science and Technology Agency

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 3, No 7, 855-882

Abstract: Abstract Discretization algorithms for semiinfinite minimax problems replace the original problem, containing an infinite number of functions, by an approximation involving a finite number, and then solve the resulting approximate problem. The approximation gives rise to a discretization error, and suboptimal solution of the approximate problem gives rise to an optimization error. Accounting for both discretization and optimization errors, we determine the rate of convergence of discretization algorithms, as a computing budget tends to infinity. We find that the rate of convergence depends on the class of optimization algorithms used to solve the approximate problem as well as the policy for selecting discretization level and number of optimization iterations. We construct optimal policies that achieve the best possible rate of convergence and find that, under certain circumstances, the better rate is obtained by inexpensive gradient methods.

Keywords: Semiinfinite minimax problems; Robust optimization; Discretization algorithms; Rate of convergence; Exponential smoothing technique (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-0109-3

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