Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Felipe Alvarez

Dep. de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

Keywords

  • Convexity
  • minimax problems
  • penalty methods
  • nonuniqueness
  • optimal trajectory
  • convergence

Mathematics Subject Classification

90C25; 90C31

References

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Suggested citation

F. Alvarez. “Absolute Minimizer in Convex Programming by Exponential Penalty.” Journal of Convex Analysis 7 (2000), No. 1, 197–202. https://doi.org/10.68381/jca07010

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Published by Heldermann Verlag, 2000. Rights now held by Banach Press LLC.