Alternating Minimization Algorithms for Convex Minimization Problem with Application to Image Deblurring and Denoising

2018 ◽  
Author(s):  
Anantachai Padcharoen ◽  
Poom Kumam ◽  
Parin Chaipunya ◽  
Wiyada Kumam ◽  
Punnarai Siricharoen ◽  
...  
Keyword(s):  
Minimization Problem ◽  
Image Deblurring ◽  
Convex Minimization ◽  
Alternating Minimization ◽  
Convex Minimization Problem ◽  
Minimization Algorithms ◽  
Alternating Minimization Algorithms ◽  
Deblurring And Denoising

scholarly journals An intermixed iteration for constrained convex minimization problem and split feasibility problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kanyanee Saechou ◽  
Atid Kangtunyakarn
Keyword(s):  
Strong Convergence ◽  
Minimization Problem ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization Problem ◽  
Split Feasibility

Abstract In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

scholarly journals A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 42
Author(s):  
Suthep Suantai ◽  
Kunrada Kankam ◽  
Prasit Cholamjiak
Keyword(s):  
Hilbert Spaces ◽  
Minimization Problem ◽  
Line Search ◽  
Optimization Problem ◽  
Splitting Method ◽  
Optimal Choice ◽  
Convex Minimization ◽  
Signal Recovery ◽  
Objective Functions ◽  
Convex Minimization Problem

In this work, we aim to investigate the convex minimization problem of the sum of two objective functions. This optimization problem includes, in particular, image reconstruction and signal recovery. We then propose a new modified forward-backward splitting method without the assumption of the Lipschitz continuity of the gradient of functions by using the line search procedures. It is shown that the sequence generated by the proposed algorithm weakly converges to minimizers of the sum of two convex functions. We also provide some applications of the proposed method to compressed sensing in the frequency domain. The numerical reports show that our method has a better convergence behavior than other methods in terms of the number of iterations and CPU time. Moreover, the numerical results of the comparative analysis are also discussed to show the optimal choice of parameters in the line search.

Power Diagrams

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Computational Geometry ◽  
Convex Function ◽  
Minimization Problem ◽  
Scalar Product ◽  
Convex Minimization ◽  
Optimal Assignment ◽  
Convex Minimization Problem ◽  
Power Diagrams ◽  
Finite Dimensional ◽  
Important Notion

This chapter considers the case when the attributes are d-dimensional vectors, the matching surplus is the scalar product, the distribution of workers' attributes is continuous, and the distribution of the firms is discrete. It discusses the geometry of the optimal assignment of workers to firms and relates it to the important notion of power diagrams in computational geometry. It shows that the optimal assignment map is the gradient of a piecewise affine convex function, and the equilibrium prices of the firms are shown to be the solution to a finite-dimensional convex minimization problem. The chapter discusses how to perform this computation in practice.

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