scholarly journals An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shujun Lian ◽  
Sitong Meng ◽  
Yiju Wang
Keyword(s):  
Global Convergence ◽  
Penalty Function ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Original Problem ◽  
Solution Method ◽  
Constrained Minimization ◽  
Constrained Minimization Problem ◽  
Objective Penalty Function

For inequality constrained minimization problem, we first propose a new exact nonsmooth objective penalty function and then apply a smooth technique to the penalty function to make it smooth. It is shown that any minimizer of the smoothing objective penalty function is an approximated solution of the original problem. Based on this, we develop a solution method for the inequality constrained minimization problem and prove its global convergence. Numerical experiments are provided to show the efficiency of the proposed method.

scholarly journals A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 890
Author(s):  
Suthep Suantai ◽  
Kunrada Kankam ◽  
Prasit Cholamjiak
Keyword(s):  
Image Processing ◽  
Minimization Problem ◽  
Convex Functions ◽  
Lower Semicontinuous ◽  
Image Inpainting ◽  
Constrained Minimization ◽  
Convex Minimization Problem ◽  
Mild Conditions ◽  
Constrained Minimization Problem ◽  
Weak Convergence Theorem

In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.

Finite Strain Elastostatics With Stiffening Materials: A Constrained Minimization Model

1997 ◽  
Vol 64 (2) ◽  
pp. 440-442 ◽  
Author(s):  
S. J. Hollister ◽  
J. E. Taylor ◽  
P. D. Washabaugh
Keyword(s):  
Boundary Value Problem ◽  
Minimization Problem ◽  
Finite Strain ◽  
Necessary Conditions ◽  
Piecewise Linear ◽  
Process Parameter ◽  
Constrained Minimization ◽  
Problem Statement ◽  
Stress Strain ◽  
Constrained Minimization Problem

Finite strain elastostatics is expressed for general anisotropic, piecewise linear stiffening materials, in the form of a constrained minimization problem. The corresponding boundary value problem statement is identified with the associated necessary conditions. Total strain is represented as a superposition of variationally independent constituent fields. Net stress-strain properties in the model are implicit in terms of the parameters that define the constituents. The model accommodates specification of load fields as functions of a process parameter.

scholarly journals Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

2015 ◽  
Vol 23 (3) ◽  
pp. 41-54 ◽  
Author(s):  
Yair Censor
Keyword(s):  
Objective Function ◽  
Minimization Problem ◽  
General Principle ◽  
Objective Function Value ◽  
Constrained Minimization ◽  
Feasible Point ◽  
Research Directions ◽  
Constrained Minimization Problem

Abstract We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full edged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned by a feasibility-seeking only algorithm. We distinguish between two research directions in the superiorization methodology that nourish from the same general principle: Weak superiorization and strong superiorization and clarify their nature.

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