Contributed Session Fri.1.H 1012

Friday, 10:30 - 12:00 h, Room: H 1012

Cluster 17: Nonsmooth optimization [...]

Topics in nonsmooth nonconvex optimization


Chair: Jean-Louis Goffin



Friday, 10:30 - 10:55 h, Room: H 1012, Talk 1

Wilhelm Passarella Freire
Interior epigraph directions method for nonsmooth and nonconvex optimization via generalized augmented Lagrangian duality

Coauthors: Regina Burachik, C. Yalcin Kaya


We propose a new method, called Interior Epigraph Directions Method (IED), for constrained nonsmooth and nonconvex optimization which uses a generalized augmented Lagrangian duality scheme. The IED method takes advantage of the special structure of the epigraph of the dual function. We prove that all the accumulation points of the primal sequence generated by IED are solutions of the original problem. We carry out numerical experiments by using test problems from the literature. In particular, we study several instances of the Kissing Number Problem. Our experiments show that the quality of the solutions obtained by IED is comparable with those obtained by other solvers.



Friday, 11:00 - 11:25 h, Room: H 1012, Talk 2

Izhar Ahmad
Optimality conditions in nondifferentiable multiobjective fractional programming


A nondifferentiable multiobjective fractional programming problems is considered. Fritz John and Kuhn-Tucker type necessary and sufficient conditions are derived for a weak efficient solution. Kuhn-Tucker type necessary conditions are shown to be sufficient for a properly efficient solution. This result gives conditions under which an efficient solution is properly efficient. An example is discussed to illustrate this result.
% Key Words: Multiobjective fractional programming, nondifferentiable programming,
% efficiency, proper efficiency, convexity.



Friday, 11:30 - 11:55 h, Room: H 1012, Talk 3

Jean-Louis Goffin
Solving unconstrained nonconvex programs with ACCPM

Coauthors: Ahad Dehghani, Dominique Orban


We suggest the use of ACCPM and proximal ACCPM, well known techniques for convex
programming problems, in a sequential convex programming method
based on ACCPM and convexification techniques to tackle unconstrained
problems with a non-convex objective function, by adding a proximal term to the objectiver. We also report a comparison of our
method with some existing algorithms: the steepest descent method and nonlinear conjugate gradient algorithms.
We use a sequence of convex functions and show that the global minimizers of these convex functions converge to a local minimizer of the original nonconvex objective function f. These convex functions are minimized by using ACCPM-prox, a code developed by J. P. Vial.
We use the set problem CUTEr and tested two version of our algorithm, ACCPM\AdaotTol and ACCPM\FixTol on 158 problems of this set. The number of variables on these 158 problems varies from 2 to 20,000. This software presents ACCPM\AdaptTol as the best solver on more that 22% of the problems and it can solve approximately 85% of the problems.


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