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The pth-order optimality conditions for inequality constrained optimization problems

✍ Scribed by O.A. Brezhneva; A.A. Tret’yakov

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
143 KB
Volume
63
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we present pth-order necessary conditions for optimality for an optimization problem with inequality constraints in the finite-dimensional spaces. Models of this type arise as the discretization of optimal control problems, calculus of variations problems, and other problems. The paper addresses the degenerate (nonregular) case when the active constraint gradients are linearly dependent. In this case, the classical necessary conditions are either inapplicable or trivially satisfied with the zero multiplier corresponding to the objective function. The proposed high-order optimality conditions give new and nontrivial conditions for nonregular cases, and reduce to the classical conditions for regular cases.

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