• 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.

• 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.

• 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.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.83-89
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• 1997

In this paper we generalize the concept of normality for the problem involving set functions in a view of Jahn. The main result is that the problem with Slater's constraint qualification is normal and stable.

• 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.

• East Asian mathematical journal
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• v.39 no.5
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• pp.505-514
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• 2023

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

• 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.

• 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.

• 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 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.