• East Asian mathematical journal
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• v.27 no.1
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1533-1539
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• 2011

In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.33-40
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• 1995

A space Y is called finitely dominated if there is a finite complex K such that Y is a retract of K in the homotopy category, i.e., we require maps $i : Y \longrightarrow K and r : K \longrightarrow Y with r \circ i \simeq idy$. The following questions are very classical in topology.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.643-656
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• 2009

The family of demi-linear mappings between topological vector spaces is a meaningful extension of the family of linear operators. We establish equicontinuity results for demi-linear mappings and develop the usual theory of distributions and the usual duality theory.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• Management Science and Financial Engineering
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• v.22 no.1
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• pp.13-20
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• 2016

We investigate the optimal consumption and investment problem when a working debtor has an option to file for bankruptcy. By applying the duality approach, the closed-form solutions are obtained for the case of CRRA utility function. The optimal bankruptcy time is determined by the first hitting time when the financial wealth hits the wealth threshold derived from the optimal stopping time problem. Moreover, the numerical results show that the investment increases as the wealth approaches the threshold and the value gain from the bankruptcy option is vanished as wealth increases.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-329
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• 2008

In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

• East Asian mathematical journal
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• v.26 no.3
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.361-376
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• 2005

Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases.

• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.97-105
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• 1999

When infeasible interior-point methods are applied to large-scale linear programming problems, they become unstable and cannot solve the problems if convergence rates of primal feasibility, dual feasibility and duality gap are not well-balanced. We can balance convergence rates of primal feasibility, dual feasibility and duality gap by introducing control parameters. As a result, the stability and the efficiency of infeasible interior-point methods can be improved.