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2004•Journal of Tangshang Teachers CollegeRequires access

Newton Method for Optimization Problem with Equal Constrains Can be Improved

Cai Chun

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Abstract

The Newton-PGCG algorithm is proposed to solve the Kuhn-Tucker equations. It is such a new algorithm that every Newton step is followed by some Preconditioned Generalized Conjugate Gradient steps. The steps parameter is given in this paper. Newton-PGCG algorithm is proved quadratically convergent exactly under the same conditions ensuring the Newton algorithm quadratically convergent exactly.

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What this paper is about

The Newton-PGCG algorithm is proposed to solve the Kuhn-Tucker equations. It is such a new algorithm that every Newton step is followed by some Preconditioned Generalized Conjugate Gradient steps. The steps parameter is given in this paper. Newton-PGCG algorithm is proved quadratically convergent exactly under the same conditions ensuring the Newton algorithm quadratically convergent exactly.

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Available abstract

The Newton-PGCG algorithm is proposed to solve the Kuhn-Tucker equations. It is such a new algorithm that every Newton step is followed by some Preconditioned Generalized Conjugate Gradient steps. The steps parameter is given in this paper. Newton-PGCG algorithm is proved quadratically convergent exactly under the same conditions ensuring the Newton algorithm quadratically convergent exactly.

Key concepts: Quadratic growth, Newton's method, Mathematics, Newton's method in optimization, Conjugate gradient method, Convergence (economics), Newton fractal, Applied mathematics

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