• 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 ${\theta}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.55-61
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• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.2
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• pp.33-42
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• 1983

Outage cost inclusion in operational simulation is very important subject in generation planning. Conventional discretized one in probabilistic simulation has unavoidably insufficient modeling and costly computation time. Now that the analytic operational simulation is possible, the outage cost inclusion is desired. With this inclusion the objective function of operational simulation becomes convex, so that analytic manipulation is easier. The derivation of outage cost is made in this paper, and the effects is evaluated. Further marginal cost is mentioned.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.33-40
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• 1990

We prove that if a $weak^*$-measurable function f defined on a finite measure space into a dual Banach space is separable-like, then for every measurable set E, the $weak^*$ core of f over E is the $weak^*$ convex closed hull of the $weak^*$ essential range of f over E.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.