scholarly journals The Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraints

2018 ◽  
Vol 182 (1) ◽  
pp. 110-132 ◽  
Author(s):  
Sandy Bitterlich ◽  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Gert Wanka
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Alternating Minimization ◽  
Minimization Algorithm ◽  
Convex Optimization Problems ◽  
Alternating Minimization Algorithm ◽  
Separable Convex Optimization

scholarly journals Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Sakineh Tahmasebzadeh ◽  
Hamidreza Navidi ◽  
Alaeddin Malek
Keyword(s):  
Convex Optimization ◽  
Objective Function ◽  
Interior Point ◽  
Optimization Problems ◽  
Numerical Algorithms ◽  
Optimal Solution ◽  
Linear Constraints ◽  
Convex Optimization Problems ◽  
Novel Algorithms ◽  
Interior Point Technique

This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solving nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar idea and linearization of the objective function. The second and third algorithms are modification of the first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemes are tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithms are more efficient and converge to the correct optimal solution, while the KKY algorithm fails in some cases. Numerical results are given to illustrate the performance of the proposed algorithms.

scholarly journals Interior-point algorithms for a class of convex optimization problems

2009 ◽  
Vol 19 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Goran Lesaja ◽  
Verlynda Slaughter
Keyword(s):  
Convex Optimization ◽  
Interior Point ◽  
Original Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Quadratic Problem ◽  
Convex Optimization Problem ◽  
Convex Optimization Problems ◽  
Novel Approach ◽  
Better Than

In this paper we consider interior-point methods (IPM) for the nonlinear, convex optimization problem where the objective function is a weighted sum of reciprocals of variables subject to linear constraints (SOR). This problem appears often in various applications such as statistical stratified sampling and entropy problems, to mention just few examples. The SOR is solved using two IPMs. First, a homogeneous IPM is used to solve the Karush-Kuhn-Tucker conditions of the problem which is a standard approach. Second, a homogeneous conic quadratic IPM is used to solve the SOR as a reformulated conic quadratic problem. As far as we are aware of it, this is a novel approach not yet considered in the literature. The two approaches are then numerically tested on a set of randomly generated problems using optimization software MOSEK. They are compared by CPU time and the number of iterations, showing that the second approach works better for problems with higher dimensions. The main reason is that although the first approach increases the number of variables, the IPM exploits the structure of the conic quadratic reformulation much better than the structure of the original problem.

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