#### (A) new global minimization method using quadratic underestimator = 이차 과소평가함수를 이용한 새로운 전역 최적화 방법

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In this study, a new global optimization method is proposed for an optimization problem with twice-differentiable objectives of a single variable. The method employs a difference of convex underestimator, that is a continuous piecewise concave quadratic function. The key idea of this research is to make the quadratic concave underestimator which does not need an iterative local optimizer to determine the lower bounding value of the objective function. The proposed method is proven to have a finite $\\\\epsilon$-convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering methods. For multivariate NLPs, a new branch-and-bound algorithm was proposed, that utilized DC underestimator as a lower bounding function for a lower bounding rule. The proposed algorithm is successfully applied to unconstrained NLP minimization problems. Compared with $\\\\alpha$BB algorithm numerically, the propose algorithm requires less number of function evaluations and computational load, CPU time, since it dose not need iterative optimizer for obtaining lower bounding value of each subregion. Modified IDP which utilizes DCU as an optimization technique, is proposed for optimal control problems. The optimal control trajectory obtained by modified IDP can guarantee finite $\\\\epsilon$-convergence. For all optimal control problems, numerical solutions are obtained the similar policy compared with the solutions of other researchers. For engineering problems, fed-batch bioreactor problem and bifunctional catalyst blend optimal control problem, the optimal control trajectories and the objective function values show robust behaviors regarding random initial guesses.
Lee, Tai-Yongresearcher이태용researcher
Description
한국과학기술원 : 생명화학공학과,
Publisher
한국과학기술원
Issue Date
2007
Identifier
263453/325007  / 000985323
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 생명화학공학과, 2007.2, [ [v], 79 p. ]

Keywords

Global Minimization; Quadratic Underestimator; 이차과소평가함수; 전역 최적화; Unconstrained NLPs

URI
http://hdl.handle.net/10203/29007