• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.101-108
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• 2009

In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• 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.

• 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.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.399-402
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• 1993

In this paper, an inverse kinematics of redundant manipulators is proposed. Optimality-constraint based inverse kinematic algorithms have some problems because those algorithms are based on necessary conditions for optimality. Among the problems, switching from a maximum value to a minimum value may occur and make an inverse kinematic solution unstable while performing a given task. An inverse kinematic solution for protecting from the switchings is suggested. By sufficient conditions for optimality, the configuration space is defined as a set of regions, potentially good configuration region and potentially bad configuration region. Inverse kinematics solution within potentially good configuration region can provide joint trajectories without both singularities and switchings. Through a simulation of tracing a circle, we show the effectiveness of this inverse kinematics.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.411-423
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• 2012

A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.