S-C. Fang (Shu-Cherng)
http://repub.eur.nl/ppl/4306/
List of Publicationsenhttp://repub.eur.nl/logo.jpg
http://repub.eur.nl/
RePub, Erasmus University RepositoryAn entropic regularization approach for mathematical programs with equilibrium constraints
http://repub.eur.nl/pub/62138/
Mon, 01 Nov 2004 00:00:01 GMT<div>S.I. Birbil</div><div>S-C. Fang</div><div>J. Han</div>
A new smoothing approach based on entropic regularization is proposed for solving a mathematical program with equilibrium constraints (MPEC). With some known smoothing properties of the entropy function and keeping real practice in mind, we reformulate an MPEC problem as a smooth nonlinear programming problem. In this way, a difficult MPEC problem becomes solvable by using available nonlinear optimization software. To support our claims, we use an online solver and test the performance of the proposed approach on a set of well-known test problems.On the convergence of a population-based global optimization algorithm
http://repub.eur.nl/pub/66129/
Mon, 01 Nov 2004 00:00:01 GMT<div>S.I. Birbil</div><div>S-C. Fang</div><div>R.-L. Sheu</div>
In global optimization, a typical population-based stochastic search method works on a set of sample points from the feasible region. In this paper, we study a recently proposed method of this sort. The method utilizes an attraction-repulsion mechanism to move sample points toward optimality and is thus referred to as electromagnetism-like method (EM). The computational results showed that EM is robust in practice, so we further investigate the theoretical structure. After reviewing the original method, we present some necessary modifications for the convergence proof. We show that in the limit, the modified method converges to the vicinity of global optimum with probability one.Recursive Approximation of the High Dimensional max Function
http://repub.eur.nl/pub/267/
Tue, 21 Jan 2003 00:00:01 GMT<div>S.I. Birbil</div><div>S-C. Fang</div><div>J.B.G. Frenk</div><div>S. Zhang</div>
An alternative smoothing method for the high dimensional max function
has been studied. The proposed method is a recursive extension of the
two dimensional smoothing functions. In order to analyze the proposed
method, a theoretical framework related to smoothing methods has been
discussed. Moreover, we support our discussion by considering some
application areas. This is followed by a comparison with an
alternative well-known smoothing method.On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems
http://repub.eur.nl/pub/225/
Mon, 16 Sep 2002 00:00:01 GMT<div>S.I. Birbil</div><div>S-C. Fang</div><div>J. Han</div>
By using a smooth entropy function to approximate the non-smooth max-type function, a vertical
linear complementarity problem (VLCP) can be treated as a family of parameterized smooth
equations. A Newton-type method with a testing procedure is proposed to solve such
a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite
number of iterations, under some conditions milder than those assumed in literature. Some
computational results are included to illustrate the potential of this approach.Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints
http://repub.eur.nl/pub/224/
Fri, 13 Sep 2002 00:00:01 GMT<div>S.I. Birbil</div><div>S-C. Fang</div><div>J. Han</div>
A new smoothing approach based on entropic perturbation
is proposed for solving mathematical programs with
equilibrium constraints. Some of the desirable
properties of the smoothing function are shown. The
viability of the proposed approach is supported by a
computationalstudy on a set of well-known test problems.Solving Variational Inequalities Defined on A Domain with Infinitely Many Linear Constraints
http://repub.eur.nl/pub/219/
Tue, 06 Aug 2002 00:00:01 GMT<div>S-C. Fang</div><div>S. Wu</div><div>S.I. Birbil</div>
We study a variational inequality problem whose domain
is defined by infinitely many linear inequalities. A
discretization method and an analytic center based
inexact cutting plane method are proposed. Under proper
assumptions, the convergence results for both methods are
given. We also provide numerical examples for the
proposed methods.