scholarly journals A weighted logarithmic barrier interior-point method for linearly constrained optimization

2021 ◽  
Vol 66 (4) ◽  
pp. 783-792
Author(s):  
Selma Lamri ◽  
◽  
Bachir Merikhi ◽  
Mohamed Achache ◽  
◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Point Method ◽  
Step Size ◽  
Positive Vector ◽  
Tangent Method ◽  
Linearly Constrained ◽  
Logarithmic Barrier

In this paper, a weighted logarithmic barrier interior-point method for solving the linearly convex constrained optimization problems is presented. Unlike the classical central-path, the barrier parameter associated with the per- turbed barrier problems, is not a scalar but is a weighted positive vector. This modi cation gives a theoretical exibility on its convergence and its numerical performance. In addition, this method is of a Newton descent direction and the computation of the step-size along this direction is based on a new e cient tech- nique called the tangent method. The practical e ciency of our approach is shown by giving some numerical results.

A Noise Based Distributed Optimization Method for Multirobot Task Allocation With Multimodal Utility

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Baisravan HomChaudhuri ◽  
Manish Kumar
Keyword(s):  
Interior Point ◽  
Task Allocation ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Distributed Optimization ◽  
Computation Time ◽  
Point Method ◽  
Search Direction ◽  
Local Optima ◽  
Primal Dual

Distributed optimization methods have been used extensively in multirobot task allocation (MRTA) problems. In distributed optimization domain, most of the algorithms are developed for solving convex optimization problems. However, for complex MRTA problems, the cost function can be nonconvex and multimodal in nature with more than one minimum or maximum points. In this paper, an effort has been made to address these complex MRTA problems with multimodal cost functions in a distributed manner. The approach used in this paper is a distributed primal–dual interior point method where noise is added in the search direction as a mechanism to allow the algorithm to escape from suboptimal solutions. The search direction from the distributed primal–dual interior point method and the weighted variable updates help in the generation of feasible primal and dual solutions and in faster convergence while the noise added in the search direction helps in avoiding local optima. The optimality and the computation time of this proposed method are compared with that of the genetic algorithm (GA) and the numerical results are provided in this paper.

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