• Title/Summary/Keyword: Constraint Optimization Problem

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ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEM

  • Lee, Gue Myung;Lee, Jae Hyoung
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.433-438
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    • 2014
  • A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.

An Integration of Local Search and Constraint Programming for Solving Constraint Satisfaction Optimization Problems (제약 만족 최적화 문제의 해결을 위한 지역 탐색과 제약 프로그래밍의 결합)

  • Hwang, Jun-Ha
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.5
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    • pp.39-47
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    • 2010
  • Constraint satisfaction optimization problem is a kind of optimization problem involving cost minimization as well as complex constraints. Local search and constraint programming respectively have been used for solving such problems. In this paper, I propose a method to integrate local search and constraint programming to improve search performance. Basically, local search is used to solve the given problem. However, it is very difficult to find a feasible neighbor satisfying all the constraints when we use only local search. Therefore, I introduced constraint programming as a tool for neighbor generation. Through the experimental results using weighted N-Queens problems, I confirmed that the proposed method can significantly improve search performance.

Determination of Parameter Value in Constraint of Sparse Spectrum Fitting DOA Estimation Algorithm (희소성 스펙트럼 피팅 도래각 추정 알고리즘의 제한조건에 포함된 상수 결정법)

  • Cho, Yunseung;Paik, Ji-Woong;Lee, Joon-Ho
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.41 no.8
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    • pp.917-920
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    • 2016
  • SpSF algorithm is direction-of-arrival estimation algorithm based on sparse representation of incident signlas. Cost function to be optimized for DOA estimation is multi-dimensional nonlinear function, which is hard to handle for optimization. After some manipulation, the problem can be cast into convex optimiztion problem. Convex optimization problem tuns out to be constrained optimization problem, where the parameter in the constraint has to be determined. The solution of the convex optimization problem is dependent on the specific parameter value in the constraint. In this paper, we propose a rule-of-thumb for determining the parameter value in the constraint. Based on the fact that the noise in the array elements is complex Gaussian distributed with zero mean, the average of the Frobenius norm of the matrix in the constraint can be rigorously derived. The parameter in the constrint is set to be two times the average of the Frobenius norm of the matrix in the constraint. It is shown that the SpSF algorithm actually works with the parameter value set by the method proposed in this paper.

ON DUALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

  • Lee, Gue Myung;Kim, Moon Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.4
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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.

OPTIMALITY CONDITIONS AND DUALITY IN NONDIFFERENTIABLE ROBUST OPTIMIZATION PROBLEMS

  • Kim, Moon Hee
    • 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.

Optimization of 3G Mobile Network Design Using a Hybrid Search Strategy

  • Wu Yufei;Pierre Samuel
    • Journal of Communications and Networks
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    • v.7 no.4
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    • pp.471-477
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    • 2005
  • This paper proposes an efficient constraint-based optimization model for the design of 3G mobile networks, such as universal mobile telecommunications system (UMTS). The model concerns about finding a set of sites for locating radio network controllers (RNCs) from a set of pre-defined candidate sites, and at the same time optimally assigning node Bs to the selected RNCs. All these choices must satisfy a set of constraints and optimize an objective function. This problem is NP-hard and consequently cannot be practically solved by exact methods for real size networks. Thus, this paper proposes a hybrid search strategy for tackling this complex and combinatorial optimization problem. The proposed hybrid search strategy is composed of three phases: A constraint satisfaction method with an embedded problem-specific goal which guides the search for a good initial solution, an optimization phase using local search algorithms, such as tabu algorithm, and a post­optimization phase to improve solutions from the second phase by using a constraint optimization procedure. Computational results show that the proposed search strategy and the model are highly efficient. Optimal solutions are always obtained for small or medium sized problems. For large sized problems, the final results are on average within $5.77\%$ to $7.48\%$ of the lower bounds.

Enhancement of Computational Efficiency of Reliability Optimization Method by Approximate Evaluation of Sub-Optimization Problem (부 최적화 문제의 근사적인 계산을 통한 신뢰도 최적설계 방범의 효율개선)

  • Jeong, Do-Hyeon;Lee, Byeong-Chae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.10
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    • pp.1597-1604
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    • 2001
  • Alternative computational scheme is presented fur reliability based optimal design using a modified advanced first order second moment (AFOSH) method. Both design variables and design parameters are considered as random variables about their nominal values. Each probability constraint is transformed into a sub -optimization problem and then is resolved with the modified Hasofer- Lind-Rackwitz-Fiessler (HL-RF) method for computational efficiency and convergence. A method of design sensitivity analysis for probability constraint is presented and tested through simple examples. The suggested method is examined by solving several examples and the results are compared with those of other methods.

ON OPTIMALITY THEOREMS FOR SEMIDEFINITE LINEAR VECTOR OPTIMIZATION PROBLEMS

  • Kim, Moon Hee
    • East Asian mathematical journal
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    • v.37 no.5
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    • pp.543-551
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    • 2021
  • Recently, semidefinite optimization problems have been intensively studied since many optimization problem can be changed into the problems and the the problems are very computationable. In this paper, we consider a semidefinite linear vector optimization problem (VP) and we establish the optimality theorems for (VP), which holds without any constraint qualification.

Heuristic Backtrack Search Algorithm for Energy-efficient Clustering in Wireless Sensor Networks (무선 센서 네트웍에서 에너지 효율적인 집단화를 위한 경험적 백트랙 탐색 알고리즘)

  • Sohn, Surg-Won
    • Journal of the Korea Society of Computer and Information
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    • v.13 no.5
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    • pp.219-227
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    • 2008
  • As found in research on constraint satisfaction problems, the choice of variable ordering heuristics is crucial for effective solving of constraint optimization problems. For the special problems such as energy-efficient clustering in heterogeneous wireless sensor networks, in which cluster heads have an inclination to be near a base station, we propose a new approach based on the static preferences variable orderings and provide a pnode heuristic algorithm for a specific application. The pnode algorithm selects the next variable with the highest Preference. In our problem, the preference becomes higher when the cluster heads are closer to the optimal region, which can be obtained a Priori due to the characteristic of the problem. Since cluster heads are the most dominant sources of Power consumption in the cluster-based sensor networks, we seek to minimize energy consumption by minimizing the maximum energy dissipation at each cluster heads as well as sensor nodes. Simulation results indicate that the proposed approach is more efficient than other methods for solving constraint optimization problems with static preferences.

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