Projected affine-scaling interior-point Newton’s method with line search filter for box constrained optimization

2014 ◽  
Vol 230 ◽  
pp. 484-495 ◽  
Author(s):  
Zhujun Wang ◽  
Detong Zhu
Keyword(s):  
Constrained Optimization ◽  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Line Search ◽  
Affine Scaling ◽  
Search Filter

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search

2000 ◽  
Vol 26 (10) ◽  
pp. 1345-1368 ◽  
Author(s):  
Peter Benner ◽  
Ralph Byers ◽  
Enrique S Quintana-Ortı́ ◽  
Gregorio Quintana-Ortı́
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Riccati Equations ◽  
Parallel Computers ◽  
Algebraic Riccati Equations ◽  
Exact Line Search

Nonmonotone conic trust region method with line search technique for bound constrained optimization

2019 ◽  
Vol 53 (3) ◽  
pp. 787-805
Author(s):  
Lijuan Zhao
Keyword(s):  
Constrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Search Technique ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

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