Nonlinear perturbations for linear semi-infinite optimization problems

Marc Teboulle

doi:10.1109/cdc.1990.204070

Nonlinear perturbations for linear semi-infinite optimization problems

Marc Teboulle^*

^*Corresponding author for this work

University of Maryland, Baltimore

Research output: Contribution to journal › Conference article › peer-review

2 Scopus citations

Abstract

A perturbation method for solving semi-infinite optimization problems is introduced. The approach is to use the continuous structure of the problem rather than an a priori discretization of the constraint set. A duality theory for infinite-dimensional convex programs is used to construct a nonlinear dual problem which is a finite-dimensional unconstrained concave problem. This induced dual problem penalizes the classical semi-infinite problem. This formulation lends itself to computing a solution of the dual by Newton's type method and allows for solving both the primal and dual problems. Implementation of a primal-dual algorithm, the connection with interior point methods, and further results are briefly discussed.

Original language	English
Pages (from-to)	2477-2478
Number of pages	2
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	4
DOIs	https://doi.org/10.1109/cdc.1990.204070
State	Published - 1990
Externally published	Yes
Event	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: 5 Dec 1990 → 7 Dec 1990

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10.1109/cdc.1990.204070

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abstract = "A perturbation method for solving semi-infinite optimization problems is introduced. The approach is to use the continuous structure of the problem rather than an a priori discretization of the constraint set. A duality theory for infinite-dimensional convex programs is used to construct a nonlinear dual problem which is a finite-dimensional unconstrained concave problem. This induced dual problem penalizes the classical semi-infinite problem. This formulation lends itself to computing a solution of the dual by Newton's type method and allows for solving both the primal and dual problems. Implementation of a primal-dual algorithm, the connection with interior point methods, and further results are briefly discussed.",

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AB - A perturbation method for solving semi-infinite optimization problems is introduced. The approach is to use the continuous structure of the problem rather than an a priori discretization of the constraint set. A duality theory for infinite-dimensional convex programs is used to construct a nonlinear dual problem which is a finite-dimensional unconstrained concave problem. This induced dual problem penalizes the classical semi-infinite problem. This formulation lends itself to computing a solution of the dual by Newton's type method and allows for solving both the primal and dual problems. Implementation of a primal-dual algorithm, the connection with interior point methods, and further results are briefly discussed.

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T2 - Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)

Y2 - 5 December 1990 through 7 December 1990

ER -

Nonlinear perturbations for linear semi-infinite optimization problems

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