• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.47-56
• /
• 2012

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

• Journal of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.17-28
• /
• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.123-137
• /
• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• The Pure and Applied Mathematics
• /
• v.19 no.2
• /
• pp.179-192
• /
• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.83-99
• /
• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

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

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
• /
• v.10 no.3
• /
• pp.85-97
• /
• 2015

This study examined the effects of outside directors and CEO duality on acquisition strategies and performance of Korean firms in high-technology industry. Based on the resource dependence theory, we focused on the service and resource-dependence roles from board of directors in the process of decision-making of acquisition strategies. In addition, CEO opportunism behavior rises when CEO serves as chairperson of board and induces the negative effects on acquisition performance. Specifically, we investigated the interaction effects between outside directors ratio and CEO duality. For the period of 2004 to 2012, 246 acquisitions of Korean firms in high-technology industry were analyzed to test our intended hypotheses. Our results indicate that there exist positive relationship between outside director ratio and acquisition performance for Korean high-technology firms. Negative associations prevail between CEO duality and performance consequences of acquisitions. While outside director ratio has a positive effect on acquisition performance when there is a presence of CEO duality, negative effect prevail for outside director ratio on acquisition performance in the absence of CEO duality position to hold our interaction hypothesis. The favor of dual structure can be explained with implications referring to unity of command and strong leadership driven from CEO duality that enhances the resource dependence roles of board of directors in the context of high-technology industry acquisition behaviors rendered by Korean firms.

• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.413-428
• /
• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• Journal of applied mathematics & informatics
• /
• v.30 no.1_2
• /
• pp.111-125
• /
• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

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