• Title, Summary, Keyword: duality method

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A Survey: SDP, its Duality, Complexity and Applications (SDP의 개관: 쌍대성, 계산복잡성 및 응용)

  • 류춘호;명영수;홍성필
    • Journal of the Korean Operations Research and Management Science Society
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    • v.26 no.2
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    • pp.13-46
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    • 2001
  • SDP (Semidefinite Programming), as a sort of “cone-LP”, optimizes a linear function over the intersection of an affine space and a cone that has the origin as its apex. SDP, however, has been developed in the process of searching for better solution methods for NP-hard combinatorial optimization problems. We surveyed the basic theories necessary to understand SDP researches. First, We examined SDP duality, comparing it to LP duality, which is essential for the interior point method, Second, we showed that SDP can be optimized from an interior solution in polynomial time with a desired error limit. finally, we summarized several research papers that showed SDP can improve solution methods for some combinatorial optimization problems, and explained why SDP has become one of the most important research topics in optimization. We tried to integrate SDP theories. relatively diverse and complicated. to survey research papers with our own perspective, and thus to help researcher to pursue their SDP researches in depth.

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AN EXACT PENALTY FUNCTION METHOD FOR SOLVING A CLASS OF NONLINEAR BILEVEL PROGRAMS

  • Lv, Yibing
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1533-1539
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    • 2011
  • In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

VISCOSITY METHODS OF APPROXIMATION FOR A COMMON SOLUTION OF A FINITE FAMILY OF ACCRETIVE OPERATORS

  • Chen, Jun-Min;Zhang, Li-Juan;Fan, Tie-Gang
    • East Asian mathematical journal
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    • v.27 no.1
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    • pp.11-21
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    • 2011
  • In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

ON OPTIMAL CONTROL OF A BOUNDARY VALUE PROBLEM

  • Kim, Hongchul;Rim, Gye-Soo
    • Korean Journal of Mathematics
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    • v.6 no.1
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    • pp.27-46
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    • 1998
  • We are concerned with an optimal control problem governed by a Poisson equation in which body force acts like a control parameter. The cost functional to be optimized is taken to represent the error from the desired observation and the cost due to the control. We recast the problem into the mixed formulation to take advantage of the minimax principle for the duality method. The existence of a saddle point for the Lagrangian shall be shown and the optimality system will be derived therein. Finally, to attain an optimal control, we combine the optimality system with an operational technique. By achieving the gradient of the cost functional, a convergent algorithm based on the projected gradient method is established.

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Solution of Fuzzy Relation Equations Using Duality of Operators

  • Lai, Edmund;Park, Chan-Gook
    • 제어로봇시스템학회:학술대회논문집
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    • pp.106.2-106
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    • 2001
  • The two typical composite operations of fuzzy relation are the max-min and the min-max composite operations. It is known that the two operations can be completely dual. This paper pays attention to the nature that these two typical operations are completely dual and investigates the correlation between the max-min composite relation equation and the min-max composite relation equation. An important scheme of correlation is in the characteristic of solution sets derived from these two fuzzy relation equations. The paper explains that one of the composite fuzzy relation equations is solvable using the solution method of the other fuzzy relation equation. The above-mentioned duality plays an important role in this solution procedure. Since it is not necessary to build the solution method separately like before, calculation efficiency can be raised. Moreover, the solution for the relation ...

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An Dynamic Analysis of Quality Control in Korean Manufacturing Industry (한국제조기업 품질관리활동의 동적 분석)

  • 이순룡;이광재
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.10 no.16
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    • pp.183-195
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    • 1987
  • The effectiveness of quality control is contingent to adaptability to the present circumstance. The objectives of this study are to provide empirical data to carry out qualify control effectively. To accomplish this purpose, an empirical study was made by questionaire (mailing survey method, Feb. to Mar. in 1987). The sample is the 167 companies in Korean manufacturing industry. The main findings out of the analysis are as follows the stage of quality control is concentrated in appraisal phase, the company standard is equiped gradually in non-KS marked company and the need of economic evaluation about quality control is increased gradually. With a view to analysing of relationship between quality control and it's effect factors (company standard, KS mark, computer based information system), the methods of $\chi$$^2$ test are used. The company standard have a significant difference in top manager's altitude to duality control, operation stage of quality control. operation scope of qualify control and quality budgeting system but is insignificant with economic evaluation about duality control. Otherwise, KS mark is insignificant with the equality control activity except for operation scope. The quality information system based in computer have a significant difference in operation stage, operation scope and economic evaluation. Therefor, for the purpose of attaining effectiveness of quality control through the economic evaluation about quality control, the company standard and computer based duality information system must be utilized in quality control activity.

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Duality of Photonic Crystal Radiative Structures and Antenna Arrays

  • Bozorgi, Mahdieh;Granpayeh, Nosrat
    • Journal of the Optical Society of Korea
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    • v.14 no.4
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    • pp.438-443
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    • 2010
  • In this paper, behaviors of photonic crystal (PC) radiative structures and antenna arrays have been compared for two types of uniform and binomial excitations. Appropriate duality has been shown between them. These results can be generalized to other types of excitation and arrangement of photonic crystal radiative arrays such as linear, planar and circular arrays of three dimensional (3D) photonic crystal termination resonators. Using these results in designing photonic circuits has some advantages for shaping a particular radiative beam at the photonic crystal exit, for instance reducing the divergence angle of the main lobe in order to enhance the directivity, for better coupling, or for splitting the emitted beam, for dividing the output beam to the next devices in photonic integrated circuits (PIC). For analysis and simulation of the photonic crystal structures, the finite difference time domain (FDTD) method has been employed.