scholarly journals An Incremental Gradient Method for Large-scale Distributed Nonlinearly Constrained Optimization

2021 ◽  
Author(s):  
Harshal D. Kaushik ◽  
Farzad Yousefian
Keyword(s):  
Constrained Optimization ◽  
Gradient Method ◽  
Large Scale ◽  
Nonlinearly Constrained Optimization

QP-Based Methods for Large-Scale Nonlinearly Constrained Optimization.

1981 ◽  
Author(s):  
Philip E. Gill ◽  
Walter Murray ◽  
Michael A. Saunders ◽  
Margaret H. Wright
Keyword(s):  
Constrained Optimization ◽  
Large Scale ◽  
Nonlinearly Constrained Optimization

Sequential Quadratic Programming

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 1-51 ◽  
Author(s):  
Paul T. Boggs ◽  
Jon W. Tolle
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Sequential Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Public Domain ◽  
Large Set ◽  
Constrained Optimization Problems ◽  
Nonlinearly Constrained Optimization

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

A Projected Conjugate Gradient Method for Box-Constrained Optimization

2014 ◽  
Vol 989-994 ◽  
pp. 2406-2409
Author(s):  
Ting Feng Li ◽  
Zhi Yuan Liu ◽  
Zhao Bin Du
Keyword(s):  
Constrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Test Problems ◽  
Active Set ◽  
Nonlinear Conjugate Gradient Method ◽  
Identification Technique

In this paper, we introduce an algorithm for solving large-scale box-constrained optimization problems. At each iteration of the proposed algorithm, we first estimate the active set by means of an active set identification technique. The components of the search direction corresponding to the active set are simply defined; the other components are determined by nonlinear conjugate gradient method. Under some additional conditions, we show that the algorithm converges globally. We also report some preliminary numerical experiments to show that the proposed algorithm is practicable and effective for the test problems.

QP-BASED METHODS FOR LARGE-SCALE NONLINEARLY CONSTRAINED OPTIMIZATION

1981 ◽  
pp. 57-98 ◽  
Author(s):  
Philip E. Gill ◽  
Walter Murray ◽  
Michael A. Saunders ◽  
Margaret H. Wright
Keyword(s):  
Constrained Optimization ◽  
Large Scale ◽  
Nonlinearly Constrained Optimization

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

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