On minimax optimization problems
Copyright policy )On minimax optimization problems
We give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk + 1 functions such that a solution to the minimax problem with thosek + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.
- University of Michigan–Ann Arbor United States
- University of Michigan United States
- University of Michigan–Flint United States
Optimization, Numerical Analysis, Convex programming, Science, nonconvex optimization, Numerical and Computational Methods, Calculus of Variations and Optimal Control, convex minimax optimization, Combinatorics, Mathematical and Computational Physics, stationary points, Mathematical Methods in Physics, Nonconvex Optimization, Minimax, Existence of solutions for minimax problems, Mathematics of Computing, Stationary Points, Mathematics, Operation Research/Decision Theory
Optimization, Numerical Analysis, Convex programming, Science, nonconvex optimization, Numerical and Computational Methods, Calculus of Variations and Optimal Control, convex minimax optimization, Combinatorics, Mathematical and Computational Physics, stationary points, Mathematical Methods in Physics, Nonconvex Optimization, Minimax, Existence of solutions for minimax problems, Mathematics of Computing, Stationary Points, Mathematics, Operation Research/Decision Theory
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