Self-adaptive inexact proximal point methods
Computational Optimization and Applications
The over-relaxed proximal point algorithm based on H-maximal monotonicity design and applications
Computers & Mathematics with Applications
Generalized Eckstein-Bertsekas proximal point algorithm based on A-maximal monotonicity design
Computers & Mathematics with Applications
Approximate generalized proximal-type method for convex vector optimization problem in Banach spaces
Computers & Mathematics with Applications
Generalized Eckstein-Bertsekas proximal point algorithm involving (H,η)-monotonicity framework
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
An inexact restoration strategy for the globalization of the sSQP method
Computational Optimization and Applications
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This paper studies the convergence of the classical proximal point algorithm without assuming monotonicity of the underlying mapping. Practical conditions are given that guarantee the local convergence of the iterates to a solution ofT( x) ? 0, whereT is an arbitrary set-valued mapping from a Hilbert space to itself. In particular, when the problem is "nonsingular" in the sense thatT-1 has a Lipschitz localization around one of the solutions, local linear convergence is obtained. This kind of regularity property of variational inclusions has been extensively studied in the literature under the name ofstrong regularity, and it can be viewed as a natural generalization of classical constraint qualifications in nonlinear programming to more general problem classes. Combining the new convergence results with an abstract duality framework for variational inclusions, the author proves the local convergence of multiplier methods for a very general class of problems. This gives as special cases new convergence results for multiplier methods for nonmonotone variational inequalities and nonconvex nonlinear programming.