• Title/Summary/Keyword: Continuous programming

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CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.75-106
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    • 2008
  • In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

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MULTIOBJECTIVE CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.603-619
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    • 2009
  • Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

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The Development of Graphic User Interface Program for Optimum Design of RC Continuous Beam (RC 연속보의 최적설계를 위한 GUI 프로그램 개발)

  • 한상훈;조홍동;박중열
    • Proceedings of the Korea Concrete Institute Conference
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    • 1999.04a
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    • pp.245-250
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    • 1999
  • In this study, the development of graphic user interface(GUI) program for optimum design of RC continuous beam is dealt. Optimum design problem that satisfies strength, serviceability, durability and geometrical conditions is formulated as a non-linear programming problem(NLP) in which the objective function as well as the constraints are highly non-linear on design variables such as cross sectional dimensions and steel ratio. Optimum design problem is solved by NLP techniques namely, sequential linear programming(SLP), sequential convex programming(SCP). Numerical examples of R.C. continuous beam using GUI system are given to show usefulness of GUI system for practical design work and efficiency of algorithm for the NLP techniques.

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Development and Improvement of Scene Transition Nets(STN) GUI Simulator for Discrete-continuous Hybrid Systems

  • Tateyama, Takeshi;Chin, Hiroshi;Kawata, Seiichi;Shimomura, Yoshiki
    • International Journal of CAD/CAM
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    • v.8 no.1
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    • pp.55-62
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    • 2009
  • Scene Transition Nets(STN) is a very useful modeling method for discrete-continuous hybrid systems. However, it is difficult to write STN in standard object-oriented programming languages because STN programming requires much skill of object-oriented programming and high knowledge of STN of designers. To overcome this problem, the authors have developed a useful GUI simulator software for modeling and simulations of STN. The experimental results of a transport system including an AGV showed the availability of our software.

LIMIT ANALYSIS OF CONTINUOUS STRUCTURES USING MATHEMATICAL PROGRAMMING

  • Victor-A.Pulmano;Loi, Francis-Tin
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1992.10a
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    • pp.7-19
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    • 1992
  • An efficient approach to limit analysis is presented whereby a continuous perfectly plastic structure is replaced by a discrete mathematical model. It is formulated as a mathematical programming problem using the static theorem of plasticity. The discretization is accomplished by writing the governing equilibrium equations in finite difference form, and is combined with piecewise linearization of the nonlinear yield curve, thus converting the formulation into a linear programming exercise. Examples of reported cases involving plates and shells are solved to illustrate the ease of application of the present method, its flexibility and accuracy - features which it make attractive to practising engineers.

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A Decomposition Method for Two stage Stochstic Programming with Block Diagonal Structure (블록 대각 구조를 지닌 2단계 확률계획법의 분해원리)

  • 김태호;박순달
    • Journal of the Korean Operations Research and Management Science Society
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    • v.10 no.1
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    • pp.9-13
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    • 1985
  • This paper develops a decomposition method for stochastic programming with a block diagonal structure. Here we assume that the right-hand side random vector of each subproblem is differente each other. We first, transform this problem into a master problem, and subproblems in a similar way to Dantizig-Wolfe's Decomposition Princeple, and then solve this master problem by solving subproblems. When we solve a subproblem, we first transform this subproblem to a Deterministic Equivalent Programming (DEF). The form of DEF depends on the type of the random vector of the subproblem. We found the subproblem with finite discrete random vector can be transformed into alinear programming, that with continuous random vector into a convex quadratic programming, and that with random vector of unknown distribution and known mean and variance into a convex nonlinear programming, but the master problem is always a linear programming.

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Mixed Integer Linear Programming Model to Determine the Optimal Levels of Technical Attributes in QFD under Multi-Segment Market (다수의 마켓 세그먼트 하에서 품질기능전개 시(時) 기술특성들의 최적 값을 결정하기 위한 혼합정수계획모형)

  • Yang, Jae Young;Yoo, Jaewook
    • Korean Management Science Review
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    • v.33 no.2
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    • pp.75-87
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    • 2016
  • Quality function deployment (QFD) is a widely adopted customer-oriented product development methodology by analyzing customer requirements. It is a main activity in QFD planning process to determine the optimal values of the technical attributes (TAs) so as to achieve the customer requirements (CRs) from the House of Quality (HoQ). In most of the previous research, all the TAs in QFD are assumed to have either continuous or discrete values. In the real world applications, the continuous TAs and the discrete TAs are often mixed in QFD. In this paper, a mixed integer linear programming model is formulated to obtain the optimal values for the continuous TAs and the discrete TAs in QFD planning as well as Branch and Bound (B and B) algorithm is proposed as the solution approach. Finally, the proposed model and solution approach are illustrated with an office chair under multi-segment market, and the sensitivity analysis is performed to study how the proposed model and its solutions respond to the variation for the two elements which are budget and CRs' weights.

A Decision Tree Algorithm using Genetic Programming

  • Park, Chongsun;Ko, Young Kyong
    • Communications for Statistical Applications and Methods
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    • v.10 no.3
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    • pp.845-857
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    • 2003
  • We explore the use of genetic programming to evolve decision trees directly for classification problems with both discrete and continuous predictors. We demonstrate that the derived hypotheses of standard algorithms can substantially deviated from the optimum. This deviation is partly due to their top-down style procedures. The performance of the system is measured on a set of real and simulated data sets and compared with the performance of well-known algorithms like CHAID, CART, C5.0, and QUEST. Proposed algorithm seems to be effective in handling problems caused by top-down style procedures of existing algorithms.

COMMON FIXED POINT THEOREMS WITH APPLICATIONS TO THE SOLUTIONS OF FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING

  • Liu, Zeqing;Liu, Min;Kim, Hyeong-Kug;Kang, Shin-Min
    • Communications of the Korean Mathematical Society
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    • v.24 no.1
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    • pp.67-83
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    • 2009
  • Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

A Study on the Extension of Fuzzy Programming Solution Method (Fuzzy 계확법의 해법일반화에 관한 연구)

  • 양태용;김현준
    • Journal of the Korean Operations Research and Management Science Society
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    • v.11 no.1
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    • pp.36-43
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    • 1986
  • In this study, the fuzzy programming is extended to handle various types of membership functions by transformation of the complicated fuzzy programming problems into the equivalent crisp linear programming problems with single objective. It is well-known that the fuzzy programming problem with linear membership functions (i.e., ramp type) can be easily transformed into a linear programming problem by introducing one dummy variable to minimize the worst unwanted deviation. However, until recently not many researches have been done to handle various general types of complicated linear membership functions which might be more realistic than ramp-or triangular-type functions. In order to handle these complicated membership functions, the goal dividing concept, which is based on the fuzzy set operation (i. e., intersection and union operations), has been prepared. The linear model obtained using the goal dividing concept is more efficient and single than the previous models [4, 8]. In addition, this result can be easily applied to any nonlinear membership functions by piecewise approximation since the membership function is continuous and monotone increasing or decreasing.

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