• Industrial Engineering and Management Systems
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• 제9권1호
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• pp.10-19
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• 2010

This paper presents an extended computing procedure for the global optimization of the triple response system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the input factors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximated using a nonlinear mathematical program involving one primary (objective) function and two secondary (constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers of target (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrange multiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensure global optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. In the field of numerical optimization, as the family of TR approach always exhibits excellent mathematical properties during optimization steps, thus the proposed algorithm can guarantee the global optimal solution where the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustrated in terms of examples found in the quality literature where the comparison results with a gradient-based method are used to calibrate TRSALG.

• 대한조선학회논문집
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• 제34권1호
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• pp.93-101
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• 1997

본 연구에서는 전통적인 비선형 최적화 기법의 문제점을 극복하기 위하여 유전자알고리즘과 지식베이스의 통합을 통한 새로운 개념의 최적화 기법을 개발하였다. 여기에서는 제한조건이 있는 비선형 최적화 문제를 해결하기 위해 사용되는 전통적인 순차적 선형화 방법과 새로운 유전자 알고리즘의 장단점을 서로 보완한 하이브리드형 최적화 기법을 개발하였다. 여기에 지식베이스를 통한 최적화 지원 기법 및 최적화 모델의 자동생성 모듈을 개발하여 최적화 모텔의 성능을 한층 개선할 수 있었다. 개발된 최적화 기법의 검증을 위하여 수학적 비선형 모델을 이용한 여러가지 기법의 비교 검토를 수행하였다.

• 대한기계학회논문집A
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• 제26권10호
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• pp.2150-2158
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• 2002

A recent research and development has the requirement for the optimization to shorten design time of modified or new product model and to obtain more precise engineering solution. General optimization problem must consider many conflicted objective functions simultaneously. Multi-objective optimization treats the multiple objective functions and constraints with design change. But, real engineering problem doesn't describe accurate constraint and objective function owing to the limit of representation. Therefore this study applies variance analysis on the basis of structure analysis and DOE to the vertical roller mill fur portland cement and proposed statistical design model to evaluate the effect of structural modification with design change by performing practical multi-objective optimization considering mass, stress and deflection.

• 대한수학회보
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• 제49권2호
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• pp.249-262
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• 2012

In this paper, under some suitable conditions and in virtue of a selection which depends on a vector-valued function and a feasible set map, the sensitivity analysis of a class of implicit multifunctions is investigated. Moreover, by using the results established, the solution sets of parametric vector optimization problems are studied.

• 대한수학회논문집
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• 제28권2호
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• 대한수학회보
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• 제50권5호
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• pp.1639-1650
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• 2013

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

• 대한수학회지
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• 제47권1호
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• pp.63-70
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• 2010

In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.

• East Asian mathematical journal
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• 제32권5호
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• pp.635-639
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• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• 대한수학회보
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• 제28권2호
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• pp.243-254
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• 1991

For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2000년도 하계학술대회 논문집
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• pp.707-710
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• 2000

Optimization of the biphenyl chloromethylation process with para-formaldehyde has been investigated in the presence of ZnCl$_2$with HCI gas by the Box-Wilson method of mathematical planning of experiment. The 4,4'- (dichloromethyl)-biphenyl yield dependence on the biphenyl para-formaldehyde ratio, temperature and reaction duration has been studied. A mathematical model of the process has been developed and optimal conditions for the biphenyl chloromethylation procedure has been determined.