scholarly journals An Accelerated Proximal Algorithm for the Difference of Convex Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Feichao Shen ◽  
Ying Zhang ◽  
Xueyong Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Optimization Problem ◽  
Proximal Algorithm ◽  
Proximal Point ◽  
Difference Of Convex Programming ◽  
Difference Of Convex ◽  
The Difference ◽  
The Given ◽  
Dc Decomposition

In this paper, we propose an accelerated proximal point algorithm for the difference of convex (DC) optimization problem by combining the extrapolation technique with the proximal difference of convex algorithm. By making full use of the special structure of DC decomposition and the information of stepsize, we prove that the proposed algorithm converges at rate of O 1 / k 2 under milder conditions. The given numerical experiments show the superiority of the proposed algorithm to some existing algorithms.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2012 ◽  
pp. 158-168
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2010 ◽  
Vol 1 (3) ◽  
pp. 1-13
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

scholarly journals Proximal point algorithm for differentiable quasi-convex multiobjective optimization

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2367-2376
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Narin Petrot
Keyword(s):  
Multiobjective Optimization ◽  
Objective Function ◽  
Critical Points ◽  
Proximal Point Algorithm ◽  
Optimization Problem ◽  
Proximal Point Method ◽  
Multiobjective Optimization Problem ◽  
Proximal Point ◽  
Accumulation Points ◽  
Locally Lipschitz

The main aim of this paper is to consider the proximal point method for solving multiobjective optimization problem under the differentiability, locally Lipschitz and quasi-convex conditions of the objective function. The control conditions to guarantee that the accumulation points of any generated sequence, are Pareto critical points are provided.

An experimental study of a DC optimization algorithm for bimatrix games

2020 ◽  
pp. 2150143
Author(s):  
Aicha Anzi ◽  
Ramzi Kasri ◽  
Hicham Lenouar ◽  
Mohammed Said Radjef
Keyword(s):  
Experimental Study ◽  
Nash Equilibrium ◽  
Linear Complementarity Problem ◽  
Optimization Algorithm ◽  
Numerical Experiments ◽  
General Scheme ◽  
Linear Complementarity ◽  
Bimatrix Games ◽  
Difference Of Convex ◽  
The Difference

This paper presents a nonconvex approach for computing a Nash equilibrium in bimatrix games. It relies on the Linear Complementarity Problem (LCP) formulation of the game and follows the Difference of Convex Algorithm (DCA) general scheme. To measure the performance of the proposed approach, numerical experiments as well as a comparative study with the Lemke Howson (LH) algorithm are carried out.

scholarly journals An extension of the proximal point algorithm beyond convexity

2021 ◽  
Author(s):  
Sorin-Mihai Grad ◽  
Felipe Lara
Keyword(s):  
Convex Functions ◽  
Proximal Point Algorithm ◽  
Lower Semicontinuous ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Proximal Point ◽  
Difference Of Convex Functions ◽  
Firmly Nonexpansive ◽  
Difference Of Convex ◽  
The One

AbstractWe introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however none of these classes fully contains the one of prox-convex functions or is included into it. We show that the classical proximal point algorithm remains convergent when the convexity of the proper lower semicontinuous function to be minimized is relaxed to prox-convexity.

scholarly journals A Hybrid Proximal Algorithm for the Sum of Monotone Operators with Multivalued Mappings

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
N. Kaewyong ◽  
L. Kittiratanawasin ◽  
C. Pukdeboon ◽  
K. Sitthithakerngkiet
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Splitting Method ◽  
Zero Point ◽  
Monotone Operators ◽  
Multivalued Mappings ◽  
Strong Convergence Theorem ◽  
Proximal Algorithm ◽  
Proximal Point

We modify a hybrid method and a proximal point algorithm to iteratively find a zero point of the sum of two monotone operators and fixed point of nonspreading multivalued mappings in a Hilbert space by using the technique of forward-backward splitting method. The strong convergence theorem is established and the illustrative numerical example is presented on this work. The results of this paper extend and improve some well-known results in the literature.

scholarly journals Inexact Inertial Proximal Algorithm for Maximal Monotone Operators

2015 ◽  
Vol 23 (2) ◽  
pp. 133-146
Author(s):  
Hadi Khatibzadeh ◽  
Sajad Ranjbar
Keyword(s):  
Nonlinear Oscillator ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Proximal Algorithm ◽  
Weak And Strong Convergence ◽  
Proximal Point ◽  
Convergence Results ◽  
Inertial Proximal Algorithm

Abstract In this paper, convergence of the sequence generated by the inexact form of the inertial proximal algorithm is studied. This algorithm which is obtained by the discretization of a nonlinear oscillator with damping dynamical system, has been introduced by Alvarez and Attouch (2001) and Jules and Maingé (2002) for the approximation of a zero of a maximal monotone operator. We establish weak and strong convergence results for the inexact inertial proximal algorithm with and without the summability assumption on errors, under different conditions on parameters. Our theorems extend the results on the inertial proximal algorithm established by Alvarez and Attouch (2001) and rules and Maingé (2002) as well as the results on the standard proximal point algorithm established by Brézis and Lions (1978), Lions (1978), Djafari Rouhani and Khatibzadeh (2008) and Khatibzadeh (2012). We also answer questions of Alvarez and Attouch (2001).

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems
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