Le Thi Hoai An

A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem

This paper is devoted to difference of convex functions (d.c.) optimization: d. c. duality, local and global optimality conditions in d. c. programming, the d. c. algorithm (DCA), and its application to solving the trust-region problem. The DCA is an iterative method that is quite different from well-known related algorithms. Thanks to the particular structure of the trust-region problem, the DCA is very simple (requiring only matrix-vector products) and, in practice, converges to the global solution. The inexpensive implicitly restarted Lanczos method of Sorensen is used to check the optimality of solutions provided by the DCA. When a nonglobal solution is found, a simple numerical procedure is introduced both to find a feasible point having a smaller objective value and to restart the DCA at this point. It is shown that in the nonconvex case, the DCA converges to the global solution of the trust-region problem, using only matrix-vector products and requiring at most 2m+2 restarts, where m is the number of distinct negative eigenvalues of the coefficient matrix that defines the problem. Numerical simulations establish the robustness and efficiency of the DCA compared to standard related methods, especially for large-scale problems.

Large-Scale Molecular Optimization from Distance Matrices by a D. C. Optimization Approach

A so-called DCA method based on a d.c.\ (difference of convex functions) optimization approach (algorithm) for solving large-scale distance geometry problems is developed. Different formulations of equivalent d.c.\ programs in the

D.C. programming approach for multicommodity network optimization problems with step increasing cost functions

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A new algorithm for Solving Large Scale Molecular Distance Geometry Problems

-approach are stated via the Lagrangian duality without gap relative to d.c.\ programming, and new nonstandard nonsmooth reformulations in the

Network utility maximisation: A DC programming approach for Sigmoidal utility function

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On the ill-posedness of the trust region subproblem

-approach (resp., the

Solving an Inverse Problem for an Elliptic Equation by d.c. Programming

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Large Scale Molecular Conformation via the Exact Distance Geometry Problem

-approach) are introduced. Substantial subdifferential calculations permit us to compute sequences of iterations in the DCA quite simply. The computations actually require matrix-vector products and only one Cholesky factorization (resp., with an additional solution of a convex program) in the

On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method

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STABILITE DE LA DUALITE LAGRANGIENNE EN OPTIMISATION D.C. (DIFFERENCE DE DEUX FONCTIONS CONVEXES)

-approach (resp., the