scholarly journals A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

2002 ◽  
Vol 92 (3) ◽  
pp. 393-424
Author(s):  
J. Charles Gilbert ◽  
Paul Armand ◽  
Sophie Jan-J�gou
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Exact Penalty ◽  
Strongly Convex ◽  
Convex Optimization Problems ◽  
Penalty Approach ◽  
Strongly Convex Optimization

scholarly journals On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces

2021 ◽  
Author(s):  
Jakub Wiktor Both
Keyword(s):  
Convex Optimization ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Linear Convergence ◽  
Rates Of Convergence ◽  
Strong Convexity ◽  
Quadratic Functional ◽  
Alternating Minimization ◽  
Strongly Convex ◽  
Strongly Convex Optimization

AbstractIn this paper, the convergence of the fundamental alternating minimization is established for non-smooth non-strongly convex optimization problems in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth, and a block-separable, non-smooth part is considered, covering a large range of applications. For the former, three different relaxations of strong convexity are considered: (i) quasi-strong convexity; (ii) quadratic functional growth; and (iii) plain convexity. With new and improved rates benefiting from both separate steps of the scheme, linear convergence is proved for (i) and (ii), whereas sublinear convergence is showed for (iii).

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