• East Asian mathematical journal
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• 제31권3호
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• pp.371-377
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• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• 한국가시화정보학회지
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• 제22권3호
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• pp.29-36
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• 2024

Topology optimization is vital in the conceptual design of various functional devices. While for thermal fluid problems, it is challenging to manage the trade-off between maximizing heat exchange and minimizing power consumption. This paper studies the individual, summation, and logarithmic summations of two conflicting objective functions in a self-developed topology optimization program for a liquid-cooled cold plate design problem. The optimized results show that the logarithmic summations provide good convergence toward the dual-objective numerical oscillations, generating smooth and continuous channel layouts. Meanwhile, it can be extended to customized layouts under the control of weighted factors. A comparison study is conducted with a conventional parallel-cooling cold plate design to validate the optimized design. Higher heat transfer coefficients and lower pressure drop are observed from the simulation results, thereby highlighting the superiority of the optimized design.

• 충청수학회지
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• 제30권1호
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• pp.31-40
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• 2017

In this paper, we consider a nonsmooth multiobjective robust optimization problem with more than two locally Lipschitz objective functions and locally Lipschitz constraint functions in the face of data uncertainty. We prove a nonsmooth sufficient optimality theorem for a weakly robust efficient solution of the problem. We formulate a Wolfe type dual problem for the problem, and establish duality theorems which hold between the problem and its Wolfe type dual problem.

• 충청수학회지
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• 제26권4호
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• pp.723-734
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• 2013

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

• 가정과삶의질연구
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• 제17권1호
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• pp.87-102
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• 1999

The purpose of this study is to discuss Faimly Business. Family Business means a business that is owned and managed by one or more family members,. Family Business is defined as one in which at 51% of the business is owned by a single family and at least one and more family members are involved in the management activities in addition to which transfer of leadership to next generation family member is anticipated. This study is to examine a clear understanding of the relationship between family functioning and business viability in families who own and operate businesses. The Overall objectives of this study are first to introduce the Family Business in the Home Economics Consumer Studies and Family Resource Management field second to theoretically review definition of Family business and related concepts bivalent attributes of Family Business the dual relationship of the social and business functions in the Family Business the dual relationship of the social and business fun tions in the Family Business, Family Business is characterized by the dual relationship of two naturally separate functions; the social function(the family) and the business function(the family business). The family in it's social function satisfies different social and emotional needs. On the other hand the business function is result-oriented the decision -marking process and behavioral pattern must be based on an objective economic model in order for the family business to compete and survive It's important to handle the overlap between the social and the business functions of Family Business and offers some guidelines on how to address with the overlap problems This study is a useful instrument for researcher educators practitioners and policy makers.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• East Asian mathematical journal
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• 제27권5호
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• pp.539-543
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• 2011

In this paper, we consider an optimization problem which consists a nonconvex quadratic objective function and two nonconvex quadratic constraint functions. We formulate its dual problem with semidefinite constraints, and we establish weak and strong duality theorems which hold between these two problems. And we give an example to illustrate our duality results. It is worth while noticing that our weak and strong duality theorems hold without convexity assumptions.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.211-225
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• 2004

A mixed type dual to a programming problem containing support functions in a objective as well as constraint functions is formulated and various duality results are validated under generalized convexity and invexity conditions. Several known results are deducted as special cases.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 춘계학술대회 논문집
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• pp.141-146
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• 1999

A new method, so called MMA(Method of Moving Asymptotes) was applied to the optimization problems of non-linear functions and non-linear structures. In each step of the iterative process, tile MMA generates a strictly convex approximation subproblems and solves them by using the dual problems. The generation of these subproblems is controlled by so called 'moving asymptotes', which may both make no oscillation and speed up tile convergence rate of optimization process. By contrast in generalized dual function, the generated function by MMA is always explicit type. Both the objective and behaviour constraints which were approximated are optimized by dual function. As the results of some examples, it was found that this method is very effective to obtain the global solution for problems with many local solutions. Also it was found that MMA is a very effective approximate method using the original function and its 1st derivatives.

• International Journal of Aeronautical and Space Sciences
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• 제18권3호
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• pp.579-587
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• 2017

Spaceborne cryocoolers produce undesirable micro-vibration disturbances during their on-orbit operation, which are a primary source of image-quality degradation for high-resolution observation satellites. Therefore, to comply with the strict mission requirement of high-quality image acquisition, micro-vibration disturbances induced by cooler operation have always been subjected to an isolation objective. However, in this study, we focused on the applicability of energy harvesting technology to generate electrical energy from micro-vibration energy of the cooler and investigated the feasibility of utilizing harvested energy as a power source to operate low-power-consumption devices such as micro-electromechanical system (MEMS) devices. A tuned mass damper (TMD)-type electromagnetic energy harvester combined with a conventional passive vibration isolator was proposed to achieve this objective. The system performs the dual functions of electrical energy generation and micro-vibration isolation. The effectiveness of the strategy was evaluated through numerical simulations.