Penalty-proximal methods in convex programming

DOI10.1007/BF00939042zbMath0622.90065OpenAlexW2046761809MaRDI QIDQ1091267

P. Fedit, Alfred Auslender, Jean-Pierre Crouzeix

Publication date: 1987

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00939042

zbMATH Keywords

convergence analysisproximal methodconstrained nonsmooth convex programs

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Methods of successive quadratic programming type (90C55)

Related Items (25)

Convergence of diagonally stationary sequences in convex optimization ⋮ Proximal interior point approach in convex programming (ill-posed problems)^*† ⋮ Survey of Bundle Methods for Nonsmooth Optimization ⋮ Coupling proximal methods and variational convergence ⋮ A continuation method for monotone variational inequalities ⋮ Equilibrium programming using proximal-like algorithms ⋮ Family of perturbation methods for variational inequalities ⋮ On the convergence of the proximal algorithm for saddle-point problems ⋮ Coupling the proximal point algorithm with approximation methods ⋮ Theoretical aspect of diagonal Bregman proximal methods ⋮ Alternating forward-backward splitting for linearly constrained optimization problems ⋮ Coupling the gradient method with a general exterior penalization scheme for convex minimization ⋮ Dual convergence for penalty algorithms in convex programming ⋮ Iterative regularization via dual diagonal descent ⋮ Alternating proximal algorithms for linearly constrained variational inequalities: application to domain decomposition for PDE's ⋮ Lagrangian-penalization algorithm for constrained optimization and variational inequalities ⋮ Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization ⋮ Penalization in non-classical convex programming via variational convergence ⋮ Computing proximal points of nonconvex functions ⋮ Lagrangian penalization scheme with parallel forward-backward splitting ⋮ Proximal-type methods with generalized Bregman functions and applications to generalized fractional programming ⋮ The perturbed Tikhonov's algorithm and some of its applications ⋮ Proximal methods in view of interior-point strategies ⋮ Prox-regularization and solution of ill-posed elliptic variational inequalities ⋮ The perturbed proximal point algorithm and some of its applications

Cites Work

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• An algorithm for linearly constrained convex nondifferentiable minimization problems
• A descent algorithm for nonsmooth convex optimization
• A Superlinearly Convergent Algorithm for One-Dimensional Constrained Minimization Problems with Convex Functions
• Iterative Solution of Linear Programs
• Necessary and sufficient conditions for a penalty method to be exact
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Numerical methods for nondifferentiable convex optimization
• An Exact Penalty Function Algorithm for Non-smooth Convex Constrained Minimization Problems
• Programmation mathématique convexe
• Convex Analysis

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