• 대한수학회지
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• 제45권2호
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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.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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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.

• East Asian mathematical journal
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• 제26권3호
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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.

• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

• 한국광학회지
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• 제4권1호
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• pp.120-131
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• 1993

빛이 갖는 파동/입자 이중성을 물리학적 사고의 발전과 비교하면서 기술하였다. 아인슈타인으로부터 현대 양자광학까지 빛에 대한 이론의 변천을 추적하고, 각 이론을 지지하는 실험적 사실을 열거하였다. 아울러 양자역학이 갖는 미묘한 측면을 지적하고, 그 개념적 기반을 서술하였다.

• 대한수학회지
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• 제46권3호
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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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• 제35권1_2호
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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).

• 대한수학회논문집
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• 제34권4호
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• pp.1353-1364
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• 2019

Modified Lagrange functional for solving an elastic problem with a crack is considered. Two formulations of a crack problem are investigated. The first formulation concerns a problem where a crack extending to the outer boundary of the domain. In the second formulation, we consider a problem with an internal crack. Duality ratio is established for initial and dual problem in both cases.

• 한국국방경영분석학회지
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• 제25권2호
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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.

• East Asian mathematical journal
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• 제27권1호
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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.