scholarly journals Sharp Primal Superlinear Convergence Results for Some Newtonian Methods for Constrained Optimization

2010 ◽  
Vol 20 (6) ◽  
pp. 3312-3334 ◽  
Author(s):  
D. Fernández ◽  
A. F. Izmailov ◽  
M. V. Solodov
Keyword(s):  
Constrained Optimization ◽  
Superlinear Convergence ◽  
Convergence Results

A Filter-Based Evolutionary Algorithm for Constrained Optimization

2005 ◽  
Vol 13 (3) ◽  
pp. 329-352 ◽  
Author(s):  
Lauren Clevenger ◽  
Lauren Ferguson ◽  
William E. Hart
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Nonlinear Problems ◽  
Pattern Search ◽  
Solution Set ◽  
Local Optimum ◽  
Partially Ordered ◽  
Convergence Results ◽  
Pattern Search Methods ◽  
Linear And Nonlinear

We introduce a filter-based evolutionary algorithm (FEA) for constrained optimization. The filter used by an FEA explicitly imposes the concept of dominance on a partially ordered solution set. We show that the algorithm is provably robust for both linear and nonlinear problems and constraints. FEAs use a finite pattern of mutation offsets, and our analysis is closely related to recent convergence results for pattern search methods. We discuss how properties of this pattern impact the ability of an FEA to converge to a constrained local optimum.

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.

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