scholarly journals Variant Gradient Projection Methods for the Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Strong Convergence ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Projection Algorithms ◽  
Infinite Dimensional ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Gradient Projection Methods

The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu’s work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed.

scholarly journals A Hybrid Gradient-Projection Algorithm for Averaged Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ming Tian ◽  
Min-Min Li
Keyword(s):  
Hilbert Spaces ◽  
Gradient Projection ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Constrained Convex Minimization ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Averaged Mappings ◽  
General Iterative Method

It is well known that the gradient-projection algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.

scholarly journals Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-26
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Hilbert Space ◽  
Gradient Projection ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Constrained Convex Minimization ◽  
Minimization Problems ◽  
Gradient Projection Algorithm ◽  
Convex Minimization Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems in a real Hilbert space. It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space.

scholarly journals A New Fast Algorithm for Constrained Four-Directional Total Variation Image Denoising Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Fan Liao ◽  
Jean Louis Coatrieux ◽  
Jiasong Wu ◽  
Huazhong Shu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Signal To Noise Ratio ◽  
Projection Methods ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Nonlocal Total Variation ◽  
Fast Gradient ◽  
Gradient Projection Methods ◽  
Generalized Variation

A new four-directional total variation (4-TV) model, applicable to isotropic and anisotropic TV functions, is proposed for image denoising. A dual based fast gradient projection algorithm for the constrained 4-TV image denoising problem is also reported which combines the well-known gradient projection and the fast gradient projection methods. Experimental results show that this model provides in most cases a better signal to noise ratio when compared to previous models like the reference TV, the total generalized variation, and the nonlocal total variation.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

Sign in / Sign up

Export Citation Format

Share Document