• Korean Journal of Mathematics
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• v.30 no.3
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• Journal of Electrical Engineering and Technology
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• v.11 no.5
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• pp.1404-1411
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• 2016

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.10
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• pp.4864-4882
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• 2016

In this work, we consider the optimization problem of minimizing energy consumption for real-time multicast over wireless multi-hop networks. Previously, a distributed primal-dual subgradient algorithm was used for finding a solution to the optimization problem. However, the traditional subgradient algorithms have drawbacks in terms of i) sensitivity to iteration parameters; ii) need for saving previous iteration results for computing the optimization results at the current iteration. To overcome these drawbacks, using a joint network coding and scheduling optimization framework, we propose a novel distributed primal-dual Random Deflected Subgradient (RDS) algorithm for solving the optimization problem. Furthermore, we derive the corresponding recursive formulas for the proposed RDS algorithm, which are useful for practical applications. In comparison with the traditional subgradient algorithms, the illustrated performance results show that the proposed RDS algorithm can achieve an improved optimal solution. Moreover, the proposed algorithm is stable and robust against the choice of parameter values used in the algorithm.

• IE interfaces
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• v.12 no.2
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• pp.337-345
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• 1999

This paper presents the optimization of a drilling operation subject to machining constraints such as power, torque, thrust, speed and feed rate. The optimization is meant to minimize the machining time required to produce a hole. For the first time, the effects of a pilot hole are included in the formulation of the machining constraints. The optimization problem is solved by using the geometric programming technique. The dual problem is simplified based on the characteristics of the problem, and the effects of machining constraints on the machining variables are identified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.41-53
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• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.981-1000
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• 2009

This paper considers asset liability management problems when their deterministic equivalent formulations are general nonlinear optimization problems. The presented approach uses a nonmonotone trust region strategy for solving a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved approximately. The algorithm does not restrict a monotonic decrease of the objective function value at each iteration. If a trial step is not accepted, the algorithm performs a non monotone line search to find a new acceptable point instead of resolving the subproblem. We prove that the algorithm globally converges to a point satisfying the second-order necessary optimality conditions.

• Journal of Korean Institute of Industrial Engineers
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• v.43 no.3
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• pp.164-175
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• 2017

Dual response surface optimization (DRSO) attempts to optimize mean and variability of a process response variable using a response surface methodology. In general, mean and variability of the response variable are often in conflict. In such a case, the process engineer need to understand the tradeoffs between the mean and variability in order to obtain a satisfactory solution. Recently, a Posterior preference articulation approach to DRSO (P-DRSO) has been proposed. P-DRSO generates a number of non-dominated solutions and allows the process engineer to select the most preferred solution. By observing the non-dominated solutions, the DM can explore and better understand the trade-offs between the mean and variability. However, the non-dominated solutions generated by the existing P-DRSO is often incomprehensive and unevenly distributed which limits the practicability of the method. In this regard, we propose a modified P-DRSO using multiple objective genetic algorithms. The proposed method has an advantage in that it generates comprehensive and evenly distributed non-dominated solutions.

• Journal of Korean Society for Quality Management
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• v.42 no.4
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• pp.685-700
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• 2014

Purpose: The purpose of this paper is to develop a systematic weighting procedure based on process capability indices method applying weighted mean squared error minimization (WMSE) approach to dual response surface optimization. Methods: The proposed procedure consists of 5 steps. Step 1 is to prepare the alternative vectors. Step 2 is to rank the vectors based on process capability indices in a pairwise manner. Step 3 is to transform the pairwise rankings into the inequalities between the corresponding WMSE values. Step 4 is to obtain the weight value by calculating the inequalities. Or, step 5 is to obtain the weight value by minimizing the total violation amount, in case there is no weight value in step 4. Results: The typical 4 process capability indices, namely, $C_p$, $C_{pk}$, $C_{pm}$, $C_{pmk}$ are utilized for the proposed procedure. Conclusion: The proposed procedure can provide a weight value in WMSE based on the objective quality performance criteria, not on the decision maker's subjective judgments or experiences.

• Journal of Power Electronics
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• v.18 no.1
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• pp.45-55
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• 2018

It is usually difficult for dual-active-bridge (DAB) dc-dc converters to operate efficiently at light loads. This paper presents an in-depth analysis of a DAB with triple-phase-shift (TPS) control under the light load condition to overcome this problem. A kind of operating mode which is suitable for light load operation is analyzed in this paper. First, an analysis of the zero-voltage-switching (ZVS) constraints for the DAB converter has been carried out and a reasonable dead-band setting method has been proposed. Secondly, the basic operating characteristics of the converter are analyzed. Third, under the condition of satisfying the ZVS constraints, both the reactive power and the root mean square (RMS) value of the current are simultaneously minimized and a particle swarm optimization (PSO) algorithm is employed to analyze and solve this optimization problem. Lastly, both simulations and experiments are carried out to verify the effectiveness of the proposed method. The experimental results show that the converter can effectively achieve ZVS and improved efficiency.

• Knowledge Management Research
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• v.19 no.2
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• pp.151-162
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• 2018

Response surface methodology (RSM) is one of popular tools to support a systematic improvement of quality of design in the product and process development stages. It consists of statistical modeling and optimization tools. RSM can be viewed as a knowledge management tool in that it systemizes knowledge about a manufacturing process through a big data analysis on products and processes. The conventional RSM aims to optimize the mean of a response, whereas dual-response surface optimization (DRSO), a special case of RSM, considers not only the mean of a response but also its variability or standard deviation for optimization. Recently, a posterior preference articulation approach receives attention in the DRSO literature. The posterior approach first seeks all (or most) of the nondominated solutions with no articulation of a decision maker (DM)'s preference. The DM then selects the best one from the set of nondominated solutions a posteriori. This method has a strength that the DM can understand the trade-off between the mean and standard deviation well by looking around the nondominated solutions. A posterior method has been proposed for DRSO. It employs an interval selection strategy for the selection step. This strategy has a limitation increasing inefficiency and complexity due to too many iterations when handling a great number (e.g., thousands ~ tens of thousands) of nondominated solutions. In this paper, a TOPSIS-based method is proposed to support a simple and efficient selection of the most preferred solution. The proposed method is illustrated through a typical DRSO problem and compared with the existing posterior method.