Journal of Convex Analysis 07 (2000), No. 1, 197--202
Copyright Heldermann Verlag 2000
Absolute Minimizer in Convex Programming by Exponential Penalty
Felipe Alvarez
Dep. de Ingenieria Matemática, Universidad de Chile, Santiago, Chile
We consider a nonlinear convex program. Under some general hypotheses, we prove that approximate solutions obtained by exponential penalty converge toward a particular solution of the original convex program as the penalty parameter goes to zero. This particular solution is called the absolute minimizer and is characterized as the unique solution of a hierarchical scheme of minimax problems.
Keywords: Convexity, minimax problems, penalty methods, nonuniqueness, optimal trajectory, convergence.
MSC: 90C25; 90C31
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