• Title/Summary/Keyword: constraint qualification

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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.

A NEW CLASS OF GENERALIZED CONVEX PROGRAMMING

  • YAN ZHAOXIANG;LI SHIZHENG
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.351-360
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    • 2005
  • This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is $\eta$-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

SADDLE POINT AND GENERALIZED CONVEX DUALITY FOR MULTIOBJECTIVE PROGRAMMING

  • Yan, Zhao-Xiang;Li, Shi-Zheng
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.227-235
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    • 2004
  • In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

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.

ON THE GLOBAL CONVERGENCE OF A MODIFIED SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS

  • Liu, Bingzhuang
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1395-1407
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    • 2011
  • When a Sequential Quadratic Programming (SQP) method is used to solve the nonlinear programming problems, one of the main difficulties is that the Quadratic Programming (QP) subproblem may be incompatible. In this paper, an SQP algorithm is given by modifying the traditional QP subproblem and applying a class of $l_{\infty}$ penalty function whose penalty parameters can be adjusted automatically. The new QP subproblem is compatible. Under the extended Mangasarian-Fromovitz constraint qualification condition and the boundedness of the iterates, the algorithm is showed to be globally convergent to a KKT point of the non-linear programming problem.

ON OPTIMALITY CONDITIONS FOR ABSTRACT CONVEX VECTOR OPTIMIZATION PROBLEMS

  • Lee, Gue-Myung;Lee, Kwang-Baik
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.971-985
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    • 2007
  • A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and ${\epsilon}$-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

ROBUST SEMI-INFINITE INTERVAL-VALUED OPTIMIZATION PROBLEM WITH UNCERTAIN INEQUALITY CONSTRAINTS

  • Jaichander, Rekha R.;Ahmad, Izhar;Kummari, Krishna
    • 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.

Performance Verification of Separation Nut Type Non-explosive Separation Device for Cube Satellite Application (큐브위성 적용을 위한 분리너트형 비폭발식 구속분리장치 인증모델의 성능검증)

  • Oh, Hyun-Ung;Lee, Myeong-Jae
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.41 no.10
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    • pp.827-832
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    • 2013
  • Heating wire cutting type separation mechanism has been widely used for cube satellite applications due to its design constraints such as small size of $10cm{\times}10cm{\times}10cm$ and light weight of less than 1kg. In addition, usage of pyro technic device is not allowed for cube satellite application. The conventional methods have some disadvantages of relatively small mechanical constraint force and the system complexity for the multi-deployable systems. In this paper, a separation nut type non-explosive separation mechanism has been proposed and investigated. The effectiveness of the design has been verified through the qualification tests of the mechanism.