• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• IE interfaces
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• v.25 no.2
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• pp.153-162
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• 2012

The reliability is defined as a probability that a system will operate properly for a specified period of time under the design operating conditions without failure and it has been considered as one of the major design parameters in the field of industries. Reliability-Redundancy Optimization Problem(RROP) involves selec tion of components with multiple choices and redundancy levels for maximizing system reliability with constraints such as cost, weight, etc. However, in practice both active and cold standby redundancies may be used within a particular system design. Therefore, a redundancy strategy(active, cold standby) for each subsystem in order to maximize system reliability is considered in this study. Due to the nature of RROP, i.e. NP-hard problem, A Parallel Particle Swarm Optimization(PPSO) algorithm is proposed to solve the mathematical programming model and it gives consistently better quality solutions than existing studies for benchmark problems.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.144-151
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• 2005

We propose an optimization method to reduce the assembly time of chip mounters. Feeder arrangement and assembly sequence are determined considering the multiple feeder assignment. The problem is divided into two sub-problems: feeder arrangement problem and assembly sequence problem. We present mathematical model for each sub-problem. The clustering algorithm and assignment algorithm are applied to solve the feeder arrangement problem. The assignment algorithm and connection algorithm are applied to solve the assembly sequence problem. Simulation results are then presented to verity the usefulness of the proposed method.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1121-1137
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• 2015

High powered computers and engineering computer systems allow designers to routinely simulate complex physical phenomena. The presented work deals with the analysis of two finite element method optimization techniques (First Order Method-FOM and Subproblem Approximation Method-SAM) implemented in the individual Design Optimization module in the Ansys software to analyze the behavior of real problems. A design optimization is a difficult mathematical process, intended to find the minimum or maximum of an objective function, which is mostly based on iterative procedure. Using optimization techniques in engineering designs requires detailed knowledge of the analyzed problem but also an ability to select the appropriate optimization method. The methods embedded in advanced computer software are based on different optimization techniques and their efficiency is significantly influenced by the specific character of a problem. The efficiency, robustness and accuracy of the methods are studied through strictly convex two-dimensional optimization problem, which is represented by volume minimization of two bars' plane frame structure subjected to maximal vertical displacement limit. Advantages and disadvantages of the methods are described and some practical tips provided which could be beneficial in any efficient engineering design by using an optimization method.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-112
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• 2012

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

• East Asian mathematical journal
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• v.17 no.2
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• pp.375-383
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• 2001

In this paper we deal with the duality theory of optimality for an optimal control problem governed by a class of second order evolution equations. First we establish the dual control systems by using conjugate functions and then associate them to the original optimization problem.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.293-300
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• 2020

In this paper we study an optimal consumption, investment and retirement time choice problem of an investor who receives labor income before her voluntary retirement. And we assume that there is a negative wealth constraint which is a general version of borrowing constraint. Using convex-duality method, we provide the closed-form solutions of the optimization problem.

• Journal of the Korean Society of Safety
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• v.30 no.3
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• pp.32-37
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• 2015

In the fields of plant layout optimization, the main goal is to minimize the construction cost including pipelines as satisfying all constraints such as safety and operating issues. However, what is the lacking of considerations in previous researches is to consider proper safety and maintenance spaces for a complex plant. Based on the mathematical programming, MILP(Mixed Integer Linear Programming) problems including various constraints can be formulated to find the optimal solution which is to achieve the best economic benefits. The objective function of this problem is the sum of piping cost, pumping cost and area cost. In general, many conventional optimization solvers are used to find a MILP problem. However, it is really hard to solve this problem due to complex inequality and equality constraints, since it is impossible to use the derivatives of objective functions and constraints. To resolve this problem, the PSO (Particle Swarm Optimization), which is one of the representative sampling approaches and does not need to use derivatives of equations, is employed to find the optimal solution considering various complex constraints in this study. The EO (Ethylene Oxide) plant is tested to verify the efficacy of the proposed method.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.14-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.13-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.