Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semi-Infinite Minimax Problems
Abstract
Discretization algorithms for semi-infinite 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.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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