January  2007, 3(1): 129-138. doi: 10.3934/jimo.2007.3.129

Optimization with some uncontrollable variables: a min-equilibrium approach

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States

Received  February 2006 Revised  September 2006 Published  January 2007

Motivated by instability analysis of unstable (excited state) solutions in computational physics/chemistry, in this paper, the minimax method for solving an optimal control problem with partially uncontrollable variables is embedded into a more general min-equilibrium problem. Results in saddle critical point analysis and computation are modified to provide more information on the minimized objective values and their corresponding riskiness for one to choose in decision making. A numerical algorithm to compute such minimized objective values and their corresponding riskiness is devised. Some convergence results of the algorithm are also established.
Citation: Jianxin Zhou. Optimization with some uncontrollable variables: a min-equilibrium approach. Journal of Industrial & Management Optimization, 2007, 3 (1) : 129-138. doi: 10.3934/jimo.2007.3.129
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