A primal—dual algorithm for the Fermat—Weber problem involving gauges
Mathematical Programming: Series A and B
The Euclidean multifacility location problem
Operations Research
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Gradient Method with Retards and Generalizations
SIAM Journal on Numerical Analysis
Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization
Computational Optimization and Applications
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Locating facilities by minimax relative to closest points of demand areas
Computers and Operations Research - Location analysis
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
An Approach to Location Models Involving Sets as Existing Facilities
Mathematics of Operations Research
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
Numerische Mathematik
A New Active Set Algorithm for Box Constrained Optimization
SIAM Journal on Optimization
An affine-scaling interior-point CBB method for box-constrained optimization
Mathematical Programming: Series A and B
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We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.