• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.3-10
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• 1998

Optimization problems may be devided into geometry optimization problems and topology optimization problems. In this paper, a method using tile equivalent material properties prediction techniques of a particulate-reinforced composites is proposed for the topology optimization. This method makes use of penalty factor in order that regions with intermediate value of design variables can be penalized. The computational results being obtained from PLBA algorithm of some values of penalty factor are presented.

• East Asian mathematical journal
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• v.31 no.3
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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.

• Korean Journal of Computational Design and Engineering
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• v.10 no.2
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• pp.143-150
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• 2005

A design framework to employ the multidisciplinary design optimization technologies on a computer system has been developed and is named as the Extensible Multidisciplinary Design Integration and Optimization System (EMDIOS). The framework can not only effectively solve complex system design problems but also conveniently handle MDO problems. Since the EMDIOS exploits both state-of-the-art of computing capabilities and sophisticated optimization techniques, it can overcome many scalability and complexity problems. It can make users who are not even familiar with the optimization technology use EMDIOS easily to solve their design problems. The client of EMDIOS provides a front end for engineers to communicate the EMDIOS engine and the server controls and manages various resources luck as scheduler, analysis codes, and user interfaces. EMDIOS client supports data monitoring, design problem definition, request for analyses and other user tasks. Three main components of the EMDIOS are the Engineering Design Object Model which is a basic idea to construct EMDIOS, EMDIOS Language (EMDIO-L) which is a script language representing design problems, and visual modeling tools which can help engineers define design problems using graphical user interface. Several example problems are solved and EMDIOS has shown various capabilities such as ease of use, process integration, and optimization monitoring.

• East Asian mathematical journal
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• v.39 no.5
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• pp.505-514
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• 2023

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.869-879
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• 2022

In this paper, we consider matrix optimization problems. We investigate augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems. Following the proofs of Eckstein [3], and Eckstein and Yao [5], we prove convergence theorems for augmented Lagrangian methods of multipliers and alternating direction methods of multipliers for the problems.

• Advances in Computational Design
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• v.2 no.3
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• pp.195-210
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• 2017

Simultaneous optimization of trusses which concurrently takes into account design variables related to the size, shape and topology of the structure is recognized as highly complex optimization problems. In this class of optimization problems, it is possible to encounter several unstable mechanisms throughout the solution process. However, to obtain a feasible solution, these unstable mechanisms somehow should be rejected from the set of candidate solutions. This study proposes triangular unit based method (TUBM) instead of ground structure method, which is conventionally used in the topology optimization, to decrease the complexity of search space of simultaneous optimization of the planar truss structures. TUBM considers stability of the triangular units for 2 dimensional truss systems. In addition, integrated particle swarm optimizer (iPSO) strengthened with robust technique so called improved fly-back mechanism is employed as the optimizer tool to obtain the solution for these class of problems. The results obtained in this study show the applicability and efficiency of the TUBM combined with iPSO for the simultaneous optimization of planar truss structures.

• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• East Asian mathematical journal
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• v.33 no.3
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• pp.265-269
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• 2017

In this paper, we formulate a sufficient optimality theorem for the robust optimization problem (UP) under (V, ${\rho}$)-invexity assumption. Moreover, we formulate a Mond-Weir type dual problem for the robust optimization problem (UP) and show that the weak and strong duality hold between the primal problems and the dual problems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.171-177
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• 2013

This paper presents a fuzzy set method to enforce complementarity constraints (CCs) in a nonlinear interior point method (NIPM)-based optimization. NIPM is a Newton-type approach to nonlinear programming problems, but it adopts log-barrier functions to deal with the obstacle of managing inequality constraints. The fuzzy-enforcement method has been implemented for CCs, which can be incorporated in optimization problems for real-world applications. In this paper, numerical simulations that apply this method to power system optimal power flow problems are included.