• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.253-263
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• 1998

This study presents a method of realizing the theoretical results of Demyanov in practice on a computer in order to produce a kind of constructive evidence for his theory and a practical method of getting numerical results for quasi-differentiab1e optimization problems which may arise in industry and science. A practical result for a restricted nondifferentiable optimization problem is experimented with a simle example.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.629-632
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• 1986

Both combinatorial and parametric optimization are used in computer-aided design(CAD). The most commonly occuring parametric optimization problems in engineering design such as design of control systems, design of electric circuits are usually expressed either as differentiable or as nondifferentiable semi-infinite programming(SIP) problems. In this paper we express algorithms for a class of computer-aided design problems arising in control systems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.187-193
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• 2012

Nash Equilibrium (NE) is as useful tool for investigating a participant's strategic generation quantity in a competitive electricity market. Cournot model may give a mixed strategy NE instead of a pure strategy when transmission constraints are considered. A mixed strategy is difficult to compute, complicated to understand conceptually, and hard to implement in an electricity market practically. This paper presents that a mixed strategy does not appear in Stackelberg leader-follower model even under a transmission congestion. A solution method is proposed for the leader-follower model under a nondifferentiable space of a strategy variable. Based on the pure strategy NE with a transmission line congested, the merit of leader-follower model is shown from a social welfare point of view.

• 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.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.433-448
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• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.12
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• pp.2353-2363
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• 1994

This paper is concerned with the design of a robust digital controller using reduced-order observer on a robotic manipulator under the disturbance. In most cases of robotic manipulator since all state vectors are not measurable, the unmeasurable state vectors must be estimated or reconstructed. Other problems are caused by the nonlinear element like as nondifferentiable Coulomb friction, disturbance due to the gravitational pull, and the torsional spring effect of a link between the drive motor and the manipulator arm. The controller is based on feeding back the observable variables and the estimated state variables which are generated by the observer, and augmenting the system by additional discrete integrators. The feedback gain parameters are obtained by first applying the optimal control theory and then readjusting the feedback parameters to eliminate the limit cycle by using describing Function for nonlinear hybrid system.