On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
Discrete & Computational Geometry
Fuzzy Sets and Systems - Special issue on fuzzy optimization
The ordered weighted averaging operators: theory and applications
The ordered weighted averaging operators: theory and applications
Dual Stochastic Dominance and Related Mean-Risk Models
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
On the complexity of Schmüdgen's positivstellensatz
Journal of Complexity
Locating tree-shaped facilities using the ordered median objective
Mathematical Programming: Series A and B
Optimization of Polynomials on Compact Semialgebraic Sets
SIAM Journal on Optimization
On Extending the LP Computable Risk Measures to Account Downside Risk
Computational Optimization and Applications
Global optimization of rational functions: a semidefinite programming approach
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Exact procedures for solving the discrete ordered median problem
Computers and Operations Research
A General Global Optimization Approach for Solving Location Problems in the Plane
Journal of Global Optimization
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity
SIAM Journal on Optimization
A semidefinite programming approach to the generalized problem of moments
Mathematical Programming: Series A and B
A generalized model of equality measures in network location problems
Computers and Operations Research
Using trapezoids for representing granular objects: Applications to learning and OWA aggregation
Information Sciences: an International Journal
Convex ordered median problem with lp-norms
Computers and Operations Research
A flexible model and efficient solution strategies for discrete location problems
Discrete Applied Mathematics
On efficient WOWA optimization for decision support under risk
International Journal of Approximate Reasoning
Moments and sums of squares for polynomial optimization and related problems
Journal of Global Optimization
Fuzzy Optimization and Decision Making
Continuous location problems and Big Triangle Small Triangle: constructing better bounds
Journal of Global Optimization
Semidefinite programming for min–max problems and games
Mathematical Programming: Series A and B
Algorithmic results for ordered median problems
Operations Research Letters
Checking local optimality in constrained quadratic programming is NP-hard
Operations Research Letters
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This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are, in general, neither rational functions nor the supremum of rational functions so current results available for the minimization of rational functions cannot be applied to handle these problems. We prove that the problem can be transformed into a new problem embedded in a higher dimensional space where it admits a convenient polynomial optimization representation. This reformulation allows a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems showing that some difficult problems (convex and non-convex) that up to date could only be solved on the plane and with Euclidean distance can be reasonably solved with different @?"p-norms in finite dimensional spaces. We illustrate this methodology with some extensive computational results on constrained and unconstrained location problems.