A corrector–predictor path-following algorithm for semidefinite optimization

2014 ◽  
Vol 07 (02) ◽  
pp. 1450028 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Line Search ◽  
Optimization Problems ◽  
Path Following ◽  
Central Path ◽  
Semidefinite Optimization ◽  
Iteration Complexity ◽  
Proximity Measure ◽  
Corrector Step ◽  
Predictor Step ◽  
Path Following Algorithm

A corrector–predictor algorithm is proposed for solving semidefinite optimization problems. In each two steps, the algorithm uses the Nesterov–Todd directions. The algorithm produces a sequence of iterates in a neighborhood of the central path based on a new proximity measure. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has [Formula: see text] iteration complexity.

scholarly journals A predictor-corrector path-following algorithm for symmetric optimization based on Darvay's technique

2014 ◽  
Vol 24 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Path Following ◽  
Euclidean Jordan Algebra ◽  
Symmetric Cone ◽  
Interior Point Algorithm ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Symmetric Cone Optimization ◽  
Predictor Corrector ◽  
Corrector Step ◽  
Predictor Step

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is o(?rlogr?/?), where r is the rank of Euclidean Jordan algebra.

scholarly journals COMPUTATIONAL GRIDS TO SOLVE LARGE SCALE OPTIMIZATION PROBLEMS WITH UNCERTAIN DATA

2014 ◽  
pp. 77-81
Author(s):  
Chefi Triki ◽  
Lucio Grandinetti
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Optimization Problems ◽  
Uncertain Data ◽  
Path Following ◽  
Computational Grids ◽  
Large Scale Optimization ◽  
Scale Optimization ◽  
Performance Computing ◽  
Path Following Algorithm

In this paper we discuss the use computational grids to solve stochastic optimization problems. These problems are generally difficult to solve and are often characterized by a high number of variables and constraints. Furthermore, for some applications it is required to achieve a real-time solution. Obtaining reasonable results is a difficult objective without the use of high performance computing. Here we present a grid-enabled path-following algorithm and we discuss some experimental results.

New complexity analysis of a full Nesterov–Todd step interior-point method for semidefinite optimization

2017 ◽  
Vol 10 (04) ◽  
pp. 1750070 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Path Following ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Line Searches ◽  
Complexity Result ◽  
Primal Dual

In this paper, we propose a new primal-dual path-following interior-point method for semidefinite optimization based on a new reformulation of the nonlinear equation of the system which defines the central path. The proposed algorithm takes only full Nesterov and Todd steps and therefore no line-searches are needed for generating the new iterations. The convergence of the algorithm is established and the complexity result coincides with the best-known iteration bound for semidefinite optimization problems.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

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