Local convergence of the proximal point algorithm and multiplier methods without monotonicity

Mathematics of Operations Research

Volumn 27, Issue 1, 2002, Pages 170-191

  Pennanen, Teemu ^a  

^a HELSINKI SCHOOL OF ECONOMICS   (Finland)

Author keywords

Local convergence; Proximal point algorithm; Strong regularity

Indexed keywords

ALGORITHMS; CONFORMAL MAPPING; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; NONLINEAR PROGRAMMING;

NONCONVEX NONLINEAR PROGRAMMING;

OPERATIONS RESEARCH;

EID: 0036473820     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.27.1.170.331     Document Type: Article

References (42)

1. A general duality principle for the sum of two operators
2. Lagrangian duality and related multiplier methods for variational inequality problems
3. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
4. Convergence results of an augmented lagrangian algorithm for optimization with a combination of general equality and linear constraints
5. Extended convergence results for the method of multipliers for non-strictly binding inequality constraints
6. Characterizations of strong regularity for variational inequalities over polyhedral convex sets
7. Characterizations of Lipschitzian stability in nonlinear programming. Mathematical programming with data perturbations
8. Ample parameterization of variational inclusions
9. Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
10. Approximate iterations in Bregman-function-based proximal algorithms
11. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
12. Smooth methods of multipliers for complementarity problems
13. Applications of the method of multipliers to variational inequalities
14. The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces
15. Entropy-like proximal methods in convex programming
16. Proximal point methods and nonconvex optimization
17. Strong stability in nonlinear programming revisited
18. Strong stability staility of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization
19. On fixed points of nonexpansive piecewise isometric mappings
20. Stability of locally optimal solutions
21. Asymptotic convergence analysis of the proximal point algorithm
22. Régularisation d'inéquations variationnelles par approximations successives
23. Dualization of generalized equations of maximal monotone type
24. Strong regularity of generalized equations
25. Newton's method for a class of nonsmooth functions
26. Composition duality and maximal monotonicity
27. Linear convergence of epsilon-subgradient descent methods for a class of convex functions
28. On the maximal monotonicity of subdifferential mappings
29. Penalty methods and augmented Lagrangians in nonlinear programming
30. Conjugate Duality and Optimization
31. Monotone operators and the proximal point algorithm
32. Augmented Lagrangians and applications of the proximal point algorithm in convex programming
33. Monotone operators and augmented Lagrangian methods in nonlinear programming
34. Lagrange multipliers and variational inequalities
35. A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
36. Submonotone mappings and the proximal point algorithm
37. The perturbed proximal point algorithm and some of its applications