A supermemory gradient projection algorithm for optimization problem with nonlinear constraints

1992 ◽  
Vol 8 (4) ◽  
pp. 323-332
Author(s):  
Ziyou Gao ◽  
Guoping He
Keyword(s):  
Optimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Nonlinear Constraints ◽  
Gradient Projection Algorithm

scholarly journals A Gradient Projection Algorithm with a New Stepsize for Nonnegative Sparsity-Constrained Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ye Li ◽  
Jun Sun ◽  
Biao Qu
Keyword(s):  
Logistic Regression ◽  
Constrained Optimization ◽  
Cost Function ◽  
Optimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Constrained Optimization Problem ◽  
Gradient Projection Algorithm ◽  
Convergence Results ◽  
Sparsity Constrained Optimization

Nonnegative sparsity-constrained optimization problem arises in many fields, such as the linear compressing sensing problem and the regularized logistic regression cost function. In this paper, we introduce a new stepsize rule and establish a gradient projection algorithm. We also obtain some convergence results under milder conditions.

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.

scholarly journals A Regularized Gradient Projection Method for the Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Yao ◽  
Shin Min Kang ◽  
Wu Jigang ◽  
Pei-Xia Yang
Keyword(s):  
Projection Method ◽  
Minimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Gradient Projection Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Gradient Projection Algorithm

We investigate the following regularized gradient projection algorithmxn+1=Pc(I−γn(∇f+αnI))xn,n≥0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problemminx∈Cf(x).

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