Constrained Minimization

2021 ◽  
pp. 209-209
Keyword(s):  
Constrained Minimization

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.

Study of a primal-dual algorithm for equality constrained minimization

2014 ◽  
Vol 59 (3) ◽  
pp. 405-433 ◽  
Author(s):  
Paul Armand ◽  
Joël Benoist ◽  
Riadh Omheni ◽  
Vincent Pateloup
Keyword(s):  
Constrained Minimization ◽  
Dual Algorithm ◽  
Primal Dual
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