Browsing by Author "Gao, D. Y."

Now showing 1 - 3 of 3
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    Canonical dual approach to solving 0-1 quadratic programming problems
    Fang, S. C.; Gao, D. Y.; Sheu, R. L.; Wu, S. Y. (American Institute of Mathematical Sciences, 2008-02)
    This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the so-called canonical (perfect) dual problems, which can be solved by deterministic methods. Both global and local extrema of the primal problems can be identified by a triality theory proposed by the author. Applications to nonconvex integer programming and Boolean least squares problems are discussed. Examples are illustrated. A conjecture on NP-hard problems is proposed.
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    Solutions and optimality criteria to box constrained nonconvex minimization problems
    Gao, D. Y. (American Institute of Mathematical Sciences, 2007-05-01)
    The design of elastic structures to optimize strength and economy of materials is a fundamental problem in structural engineering and related areas of applied mathematics. In this article we explore a finite dimensional framework for approximate solution of such design problems based on linear elasticity with a range of elastic coefficients assumed available as design parameters. Solution methods for related optimization problems based on the matrix trace norm are suggested and analyzed, providing existence and uniqueness theorems. Results of computations for sample problems are presented and compared with parallel results in the literature based on other approaches.
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    Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints
    Gao, D. Y. (American Institute of Mathematical Sciences, 2005-02)
    The paper studies forced surface waves on an incompressible, inviscid fluid in a two-dimensional channel with a small negative or oscillatory bump on a rigid flat bottom. Such wave motions are determined by a non-dimensional wave speed F, called Froude number, and F = 1 is a critical value of F. If F = 1 + lambda epsilon with a small parameter epsilon > 0, then a forced Korteweg-deVries (FKdV) equation can be derived to model the wave motion on the free surface. In this paper, the case lambda > 0 (or F > 1, called supercritical case) is considered. The steady and unsteady solutions of the FKdV equation with a negative bump function independent of time are first studied both theoretically and numerically. It is shown that there are five steady solutions and only one of them, which exists for all lambda > 0, is stable. Then, solutions of the FKdV equation with an oscillatory bump function posed on R or a finite interval are considered. The corresponding linear problems are solved explicitly and the solutions are rigorously shown to be eventually periodic as time goes to infinity, while a similar result holds for the nonlinear problem posed on a finite interval with small initial data and forcing functions. The nonlinear solutions with zero initial data for any forcing functions in the real line R or large forcing functions in a finite interval are obtained numerically. It is shown numerically that the solutions will become eventually periodic in time for a small forcing function. The behavior of the solutions becomes quite irregular as time goes to infinity, if the forcing function is large.