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1976•International Journal of Systems ScienceRequires access

On Lagrange multipliers and constraints I. Lagrangian approach

Hayatoshi Sayama, Liang Fan, L. S. FAN

Open publisher page 2 citations

Abstract

This paper establishes the relations between the changes in tho values of the Lagrange multipliers and the changes in the values of tho constraint and objoetivo functions for a non-linear, convex programme based on the classical Lagrangian. Using somo Lagrange multipliers which are larger (smaller) than the optimal ones, it is possible that a point minimizing the Lagrangian is inside the feasible (infeasible) region. Illus-strativo examples are presented for quadratic programming problems.

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What this paper is about

This paper establishes the relations between the changes in tho values of the Lagrange multipliers and the changes in the values of tho constraint and objoetivo functions for a non-linear, convex programme based on the classical Lagrangian. Using somo Lagrange multipliers which are larger (smaller) than the optimal ones, it is possible that a point minimizing the Lagrangian is inside the feasible (infeasible) region. Illus-strativo examples are presented for quadratic programming problems.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper establishes the relations between the changes in tho values of the Lagrange multipliers and the changes in the values of tho constraint and objoetivo functions for a non-linear, convex programme based on the classical Lagrangian. Using somo Lagrange multipliers which are larger (smaller) than the optimal ones, it is possible that a point minimizing the Lagrangian is inside the feasible (infeasible) region. Illus-strativo examples are presented for quadratic programming problems.

Key concepts: Lagrange multiplier, Constraint algorithm, Lagrangian, Augmented Lagrangian method, Mathematics, Constraint (computer-aided design), Lagrangian point, Quadratic equation

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