A Semidefinite Programming approach for solving Multiobjective Linear Programming

Authors:
Victor Blanco;Justo Puerto;Safae El Haj Ben Ali
Affiliations:
Department of Quantitative Methods for Economics and Business, Universidad de Granada, Granada, Spain;IMUS, Universidad de Sevilla, Seville, Spain;IMUS, Universidad de Sevilla, Seville, Spain
Venue:
Journal of Global Optimization
Year:
2014

Citing 14
Cited 0

Theory of linear and integer programming

Theory of linear and integer programming
Determination of the efficient set in multiobjective linear programming

Journal of Optimization Theory and Applications
An Outer Approximation Algorithm for Generating AllEfficient Extreme Points in the Outcome Set of a Multiple ObjectiveLinear Programming Problem

Journal of Global Optimization
On the complexity of Schmüdgen's positivstellensatz

Journal of Complexity
Semidefinite representations for finite varieties

Mathematical Programming: Series A and B
On the complexity of Putinar's Positivstellensatz

Journal of Complexity
An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

Mathematics of Operations Research
Generating All Vertices of a Polyhedron Is Hard

Discrete & Computational Geometry
Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals

Foundations of Computational Mathematics
GloptiPoly 3: moments, optimization and semidefinite programming

Optimization Methods & Software - GLOBAL OPTIMIZATION
Moments and sums of squares for polynomial optimization and related problems

Journal of Global Optimization
Partial Gröbner Bases for Multiobjective Integer Linear Optimization

SIAM Journal on Discrete Mathematics
Some algebraic methods for solving multiobjective polynomial integer programs

Journal of Symbolic Computation
A dual variant of Benson's "outer approximation algorithm" for multiple objective linear programming

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions of Multiobjective Linear Programmes (MOLPs). However, all of them are based on active-set methods (simplex-like approaches). We present a different method, based on a transformation of any MOLP into a unique lifted Semidefinite Program (SDP), the solutions of which encode the entire set of Pareto-optimal extreme point solutions of any MOLP. This SDP problem can be solved, among other algorithms, by interior point methods; thus unlike an active set-method, our method provides a new approach to find the set of Pareto-optimal solutions of MOLP.