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2001•Hokkaido Mathematical JournalOpen access

Global convergence of a trust-region algorithm for inequality constrained optimization

Xiaojiao Tong, Shuzi ZHOU

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Abstract

This paper presents a trust-region algorithm for n-dimensional nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, being the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Condition $m\leq n$ is required.

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This paper presents a trust-region algorithm for n-dimensional nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, being the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Condition $m\leq n$ is required.

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Available abstract

This paper presents a trust-region algorithm for n-dimensional nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, being the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Condition $m\leq n$ is required.

Key concepts: Karush–Kuhn–Tucker conditions, Trust region, Mathematics, Convergence (economics), Mathematical optimization, Nonlinear system, Inequality, Basis (linear algebra)

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