A Lagrange Multiplier Method for Certain Constrained Min-Max Problems

Edward S. Pearsall
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Edward S. Pearsall: Wayne State University, Detroit, Michigan

Operations Research, 1976, vol. 24, issue 1, 70-91

Abstract: Constrained min-max problems are constant-sum, two-person games in which the maximizing player enjoys the advantage of moving last and both players select allocations subject to separate constraints on their use of resources. This paper presents a Lagrange multiplier method for addressing such problems where the maximizing player is permitted to mix strategies probabilistically. We derive conditions under which the method will locate optimal solutions and discuss suitable applications. A simple ABM/shelter deployment problem is solved to illustrate the essential features of the method.

Date: 1976
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