0000000000528389

AUTHOR

Jacqueline Morgan

showing 3 related works from this author

ε-Regularized two-level optimization problems: Approximation and existence results

2006

The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.

Mathematical optimizationVector optimizationWork (thermodynamics)Optimization problemL-reductionApproximation algorithmHardness of approximationConvexityPolynomial-time approximation schemeMathematics
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Least-Norm Regularization For Weak Two-Level Optimization Problems

1992

In this paper, we consider a regularization for weak two-level optimization problems by adaptation of the method presented by Solohovic (1970). Existence and approximation results are given in the case in which the constraints to the lower level problems are described by a multifunction. Convergence results for the least-norm regularization under perturbations are also presented.

Mathematical optimizationOptimization problemNorm (mathematics)Proximal gradient methods for learningRegularization perspectives on support vector machinesBackus–Gilbert methodRegularization (mathematics)Mathematics
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Approximate solutions for two-level optimization problems

1988

This paper is devoted to general results for approximating two-level optimization problems in which the set of solutions to the lower level problem is not a singleton.

Set (abstract data type)Mathematical optimizationOptimization problemStackelberg solutionSingletonApproximate solutionMathematics
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