scholarly journals Homotopy Interior-Point Method for a General Multiobjective Programming Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
X. Zhao ◽  
S. G. Zhang ◽  
Q. H. Liu
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Interior Point Method ◽  
Multiobjective Programming ◽  
Point Method ◽  
Kkt System ◽  
Basic Assumptions ◽  
Multiobjective Programming Problem ◽  
Kkt Points

We present a combined homotopy interior-point method for a general multiobjective programming problem. For solving the KKT points of the multiobjective programming problem, the homotopy equation is constructed. We prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system under some basic assumptions.

scholarly journals Homotopy Method for a General Multiobjective Programming Problem under Generalized Quasinormal Cone Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
X. Zhao ◽  
S. G. Zhang ◽  
Y. T. Yang ◽  
Q. H. Liu
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Multiobjective Programming ◽  
Continuation Method ◽  
Homotopy Continuation ◽  
Cone Condition ◽  
Kkt System ◽  
Homotopy Continuation Method ◽  
Basic Assumptions ◽  
Multiobjective Programming Problem

A combined interior point homotopy continuation method is proposed for solving general multiobjective programming problem. We prove the existence and convergence of a smooth homotopy path from almost any interior initial interior point to a solution of the KKT system under some basic assumptions.

Symbolic implementation of interior point method for linear programming problem

2010 ◽  
Vol 87 (10) ◽  
pp. 2173-2187
Author(s):  
Predrag S. Stanimirović ◽  
Nebojša V. Stojković ◽  
Ivan M. Jovanović
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Interior Point ◽  
Linear Programming Problem ◽  
Interior Point Method ◽  
Point Method

The Combined Homotopy Methods for Optimizition under the Quasi-Normal Cone Condition

2012 ◽  
Vol 459 ◽  
pp. 16-18
Author(s):  
Yun Feng Gao
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Research Field ◽  
Point Method ◽  
Convex Programming Problem ◽  
Cone Condition ◽  
Reverse Convex ◽  
Theoretical Results

Non-convex programming problem is a hot problem in research field of optimization problems, since the interior point method is applied for solving programming problem. In this paper, we use the homotopy interior point method for solving a class of optimization problems by the existing theoretical results under quasi-norm cone condition. Contrary to this partial reverse convex constrained domain, we give the structure method of the quasi-norm cone condition, construct the combined homotopy method under quasi-norm cone condition and show some numerical examples

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

scholarly journals An interior point method for isogeometric contact

2014 ◽  
Vol 276 ◽  
pp. 589-611 ◽  
Author(s):  
İ. Temizer ◽  
M.M. Abdalla ◽  
Z. Gürdal
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method
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