Matrix analysis
NP-Hard, capacitated, balanced p-median problems on a chain graph with a continuum of link demands
Mathematics of Operations Research
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
A Smoothing Newton Method for Minimizing a Sum of Euclidean Norms
SIAM Journal on Optimization
An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications
SIAM Journal on Optimization
Computational Optimization and Applications
Algorithmic approaches for solving the euclidean distance location and location-allocation problems
Algorithmic approaches for solving the euclidean distance location and location-allocation problems
A heuristic method for large-scale multi-facility location problems
Computers and Operations Research
Convex Optimization
SIAM Journal on Optimization
A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem
Mathematics of Operations Research
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
A polynomial time dual algorithm for the Euclidean multifacility location problem
Operations Research Letters
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We propose a primal-dual continuation approach for the capacitated multi-facility Weber problem (CMFWP) based on its nonlinear second-order cone program (SOCP) reformulation. The main idea of the approach is to reformulate the CMFWP as a nonlinear SOCP with a nonconvex objective function, and then introduce a logarithmic barrier term and a quadratic proximal term into the objective to construct a sequence of convexified subproblems. By this, this class of nondifferentiable and nonconvex optimization problems is converted into the solution of a sequence of nonlinear convex SOCPs. In this paper, we employ the semismooth Newton method proposed in Kanzow et al. (SIAM Journal of Optimization 20:297---320, 2009) to solve the KKT system of the resulting convex SOCPs. Preliminary numerical results are reported for eighteen test instances, which indicate that the continuation approach is promising to find a satisfying suboptimal solution, even a global optimal solution for some test problems.