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New Form of Lagrangian Multiplier Methods

Aifen Feng, Cuixia Xu, Dingguo Pu

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Abstract

The Lagrangian multiplier method is one of the important methods of solving nonlinear constraints programming. In this paper, a new class of augmented Lagrangian functions with a new NCP function is proposed for the minimization of a smooth function subject to smooth equation and inequality constraints. Under certain conditions, We prove 1-1 corresponding relationship of optimality solution between the primal constrained problem and the new unconstrained problem. Then a Algorithm is constructed to solve nonlinear constraints problem, and also prove the convergence of the algorithm.

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What this paper is about

The Lagrangian multiplier method is one of the important methods of solving nonlinear constraints programming. In this paper, a new class of augmented Lagrangian functions with a new NCP function is proposed for the minimization of a smooth function subject to smooth equation and inequality constraints. Under certain conditions, We prove 1-1 corresponding relationship of optimality solution between the primal constrained problem and the new unconstrained problem. Then a Algorithm is constructed to solve nonlinear constraints problem, and also prove the convergence of the algorithm.

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Available abstract

The Lagrangian multiplier method is one of the important methods of solving nonlinear constraints programming. In this paper, a new class of augmented Lagrangian functions with a new NCP function is proposed for the minimization of a smooth function subject to smooth equation and inequality constraints. Under certain conditions, We prove 1-1 corresponding relationship of optimality solution between the primal constrained problem and the new unconstrained problem. Then a Algorithm is constructed to solve nonlinear constraints problem, and also prove the convergence of the algorithm.

Key concepts: Augmented Lagrangian method, Lagrange multiplier, Lagrangian, Multiplier (economics), Mathematics, Mathematical optimization, Lagrangian relaxation, Convergence (economics)

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