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A Trust Region Method for Nonlinear System

Tong Jian

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Abstract

This paper presents a trust region method for nonlinear system. This problem is first transformed into a nonlinear optimization with nonnegative constraints by introducing slack variables. Then, without solving a quadratic trust region sub-problem, a system of linear equations is solved to find a search direction with the aid of to the KKT condition and F-B the NCP function. Under certain conditions, this algorithm is globally convergent and locally super-linear convergent. Numerical experiments show that the algorithm is effective.

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What this paper is about

This paper presents a trust region method for nonlinear system. This problem is first transformed into a nonlinear optimization with nonnegative constraints by introducing slack variables. Then, without solving a quadratic trust region sub-problem, a system of linear equations is solved to find a search direction with the aid of to the KKT condition and F-B the NCP function. Under certain conditions, this algorithm is globally convergent and locally super-linear convergent. Numerical experiments show that the algorithm is effective.

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Available abstract

This paper presents a trust region method for nonlinear system. This problem is first transformed into a nonlinear optimization with nonnegative constraints by introducing slack variables. Then, without solving a quadratic trust region sub-problem, a system of linear equations is solved to find a search direction with the aid of to the KKT condition and F-B the NCP function. Under certain conditions, this algorithm is globally convergent and locally super-linear convergent. Numerical experiments show that the algorithm is effective.

Key concepts: Karush–Kuhn–Tucker conditions, Trust region, Mathematics, Nonlinear system, Mathematical optimization, Function (biology), Quadratic equation, Convergence (economics)

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