THEORY OF LAGRANGE MULTIPLIERS FOR CONSTRAINED OPTIMIZATION PROBLEMS

1967 ◽  
Author(s):  
James E. Falk
Keyword(s):  
Constrained Optimization ◽  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Constrained Optimization Problems

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

scholarly journals An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

2021 ◽  
Author(s):  
Christian Kanzow ◽  
Andreas B. Raharja ◽  
Alexandra Schwartz
Keyword(s):  
Constrained Optimization ◽  
Numerical Experiments ◽  
Penalty Method ◽  
Augmented Lagrangian ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Constrained Optimization Problems ◽  
Strongly Stationary ◽  
Type Constraint

AbstractA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.

scholarly journals Equilibrium constrained optimization problems

2006 ◽  
Vol 169 (3) ◽  
pp. 1108-1127 ◽  
Author(s):  
Ş.İ. Birbil ◽  
G. Bouza ◽  
J.B.G. Frenk ◽  
G. Still
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Constrained Optimization Problems
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