Constrained optimization problems in Banach space

1975 ◽  
Vol 17 (3-4) ◽  
pp. 279-291 ◽  
Author(s):  
P. C. Das
Keyword(s):  
Banach Space ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Constrained Optimization Problems

Convergence of Subdifferentials of Convexly Composite Functions

1999 ◽  
Vol 51 (2) ◽  
pp. 250-265 ◽  
Author(s):  
C. Combari ◽  
R. Poliquin ◽  
L. Thibault
Keyword(s):  
Banach Space ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Constrained Optimization Problems ◽  
Composite Functions ◽  
Kuratowski Convergence ◽  
General Banach Space

AbstractIn this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.

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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