• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.565-573
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• 2001

In this paper, we first rove the strict quasi-concavity of maximizing function, and next prove a new maximum theorem using Fan’s generalization of the classical KKM theorem. Also an existence theorem of social equilibrium can be proved when an additional assumption on the constraint correspondence is assumed. Finally, we give illustrative two examples of constrained optimization problems.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.535-541
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• 2002

In this paper, we introduce the concept of lower semi-continuous from above functions and show that many well-known results, such as Ekland's and Caristi's theorems, remain also true under lower semi-continuous from above functions.

• Journal of the military operations research society of Korea
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• v.9 no.1
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• pp.69-74
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• 1983

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $1-{\beta}$ is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes ${\beta}\;=\;1$ and ${\beta}\;=\;0$ the model presented reduces to the usual backorders and lost sales case, respectively.

• The Journal of the Acoustical Society of Korea
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• v.16 no.3E
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• pp.62-68
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• 1997

In this paper, a modified adaptive sign (MAS) algorithm based on a mixed norm error criterion is proposed. The mixed norm error criterion of be minimized is constructed as a combined convex function of the mean-absolute error and the mean-absolute error to the third power. A convergence analysis of the MAS algorithm is also presented. Under a set of mild assumptions, a set of nonlinear evolution equations that characterizes the statistical mean and mean-squared behavior of the algorithm is derived. Computed simulations are carried out to verify the validity of our derivations.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.3
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• pp.233-236
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• 2015

In this paper, a nonlinear optimization problem is proposed to obtain a structured static output feedback controller for discrete time linear systems. The proposed optimization problem has LMI (Linear Matrix Inequality) constraints and a non-convex objective function. Using the conditional gradient method, we can obtain suboptimal solutions of the proposed optimization problem. Numerical examples show the effectives of the proposed approach.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.333-342
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• 2007

A nonsmooth PGD scheme for minimizing a nonsmooth convex function is presented. In the parallelization step of the algorithm, a method due to Pang, Han and Pangaraj (1991), [7], is employed to solve a subproblem for constructing search directions. The convergence analysis is given as well.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.399-410
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• 2010

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• Journal of Information Science Theory and Practice
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• v.1 no.3
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• pp.6-11
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• 2013

A new explanation, using exponential functions, is given for the S-shaped functional relation between the mean citation score and the proportion of top 10% (and other percentages) publications for the 500 Leiden Ranking universities. With this new model we again obtain an explanation for the concave or convex relation between the proportion of top $100{\theta}%$ publications, for different fractions of ${\theta}$.