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A linear programming based algorithm to solve a class of optimization problems with a multi-linear objective function and affine constraints

Charkhgard, H ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cor.2017.07.015
  3. Publisher: Elsevier Ltd , 2018
  4. Abstract:
  5. We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems has only one objective function, but it can also be viewed as a class of multi-objective optimization problems by decomposing its objective function. The proposed algorithm exploits this idea and solves this class of optimization problems from the viewpoint of multi-objective optimization. The algorithm computes an optimal solution when the number of variables in the multi-linear objective function is two, and an approximate solution when the number of variables is greater than two. A computational study demonstrates that when available computing time is limited the algorithm significantly outperforms well-known convex programming solvers IPOPT and CVXOPT, in terms of both efficiency and solution quality. The optimization problems in this class can be reformulated as second-order cone programs, and, therefore, also be solved by second-order cone programming solvers. This is highly effective for small and medium size instances, but we demonstrate that for large size instances with two variables in the multi-linear objective function the proposed algorithm outperforms a (commercial) second-order cone programming solver. © 2017 Elsevier Ltd
  6. Keywords:
  7. Convex programming ; Linear programming ; Multi-linear objective function ; Pareto optimal solutions ; Polynomial-time algorithm ; Computational efficiency ; Convex optimization ; Multiobjective optimization ; Optimal systems ; Pareto principle ; Polynomial approximation ; Polynomials ; Computational studies ; Linear objective functions ; Multi-objective optimization problem ; Optimization problems ; Polynomial-time algorithms ; Second order cone programs ; Second-order cone programming ; Optimization
  8. Source: Computers and Operations Research ; Volume 89 , 2018 , Pages 17-30 ; 03050548 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0305054817301995