Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints
SIAM Journal on Optimization
GRIN: An Implementation of Gröbner Bases for Integer Programming
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Buchberger Algorithm and Integer Programming
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A New Algebraic Geometry Algorithm for Integer Programming
Management Science
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A semidefinite programming approach to the generalized problem of moments
Mathematical Programming: Series A and B
An Elitist GRASP Metaheuristic for the Multi-objective Quadratic Assignment Problem
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Partial Gröbner Bases for Multiobjective Integer Linear Optimization
SIAM Journal on Discrete Mathematics
A Semidefinite Programming approach for solving Multiobjective Linear Programming
Journal of Global Optimization
| Hi-index | 0.00 |
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Grobner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.