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2003•SUT Journal of MathematicsOpen access

Local convergence properties of primal-dual interior point methods based on the shifted barrier KKT conditions for nonlinear optimization

Hiroshi Yabe, Hiroshi Yamashita

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Abstract

In this paper, we consider the shifted barrier KKT conditions for nonlinear optimization. We propose a primal-dual interior point method based on these conditions. By choosing suitable parameters used in our method, we prove local and q-quadratic convergence of the Newton interior point method, and local and q-superlinear convergence of the quasi-Newton interior point method.

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In this paper, we consider the shifted barrier KKT conditions for nonlinear optimization. We propose a primal-dual interior point method based on these conditions. By choosing suitable parameters used in our method, we prove local and q-quadratic convergence of the Newton interior point method, and local and q-superlinear convergence of the quasi-Newton interior point method.

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Available abstract

In this paper, we consider the shifted barrier KKT conditions for nonlinear optimization. We propose a primal-dual interior point method based on these conditions. By choosing suitable parameters used in our method, we prove local and q-quadratic convergence of the Newton interior point method, and local and q-superlinear convergence of the quasi-Newton interior point method.

Key concepts: Karush–Kuhn–Tucker conditions, Interior point method, Local convergence, Convergence (economics), Nonlinear system, Mathematics, Quadratic equation, Mathematical optimization

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