• International Journal of Computer Science & Network Security
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• 제24권1호
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.229-235
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• 2005

The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class $C^2$. Moreover, we find more characterizations for spherically concave functions.

• 대한산업공학회지
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• 제19권2호
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• 충청수학회지
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• 제23권4호
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• pp.657-661
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• 2010

We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

• 대한수학회보
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• 제45권1호
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• pp.39-44
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• 2008

In this paper, we introduce the concepts of pre convexity neighborhoods, c-concave functions. We study some properties for c-convex functions, and characterize c-convex functions and c-concave functions by using the preconvexity neighborhoods.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• 호남수학학술지
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• 제29권4호
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• pp.589-595
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• 2007

In this paper, we introduce the concepts of the convexity hull and co-convex sets on preconvexity spaces. We study some properties for the co-convexity hull and characterize c-convex functions and c-concave functions by using the co-convexity hull and the convexity hull.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2011년 춘계학술대회논문집
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• pp.100-103
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• 2011

In the present work, a numerical study of fluid flow and heat transfer on the concave surface with impinging jet has been performed by solving three-dimensional Reynods-averaged Naver-Stokes(RANS) equations. The constant temperature condition was applied to the concave impingement surface. The inclination angle of jet nozzle and the distance between jet nozzles are chosen as design variables under equivalent mass flow rate of working fluid into cooling channel, and area averaged Nusselt number on concave impingement surface is set as the objective function. Thirteen training points are obtained by Latin Hypercube sampling method, and the PEA model is constructed by using the objective function values at the trainging points. And, the sequential quadratic programming is used to search for the optimal paint from the PBA model. Through the optimization, the optimal shape shows improved heat transfer rate as compared to the reference geometry.

• 한국경영과학회지
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• 제22권3호
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• pp.11-22
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• 1997

The aim of this paper is to develop the B & B type algorithms for globally minimizing concave function under 0-1 knapsack constraint. The linear convex envelope underestimating the concave object function is introduced for the bounding operations which locate the vertices of the solution set. And the simplex containing the solution set is sequentially partitioned into the subsimplices over which the convex envelopes are calculated in the candidate problems. The adoption of cutting plane method enhances the efficiency of the algorithm. These mean valid inequalities with respect to the integer solution which eliminate the nonintegral points before the bounding operation. The implementations are effectively concretized in connection with the branching stategys.

• 한국컴퓨터정보학회논문지
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• 제25권7호
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• pp.75-83
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• 2020

셀룰라 시스템에서 D2D 유틸리티 최적화 문제를 연구하도록 한다. 구체적으로, Non-Convex 최적화 문제의 복잡도를 완화하도록 해주는 오목함수 결정규칙을 제안하고자 한다. 일반적으로, 유틸리티 함수는 신호와 간섭의 함수이며, 해법이 복잡한 Non-Convex 형태를 가진다. 본 논문에서는 간단한 해법을 찾고자 유틸리티 함수를 간섭관점에서 분석한다. 먼저 D2D 수신단에서의 간섭 레벨을 의미하는 '상대간섭'과 간섭을 주요간섭으로 간략화하는 '간섭주요화'를 수식적으로 정의한다. 정의한 간섭주요화를 바탕으로 간단한 해법의 기반이 되는 오목함수 결정규칙과 최적화 해법이 간단한 Convex Optimization 해법을 제안하도록 한다. 실험결과를 통하여 유틸리티 함수는 D2D 적용시나리오에 해당하는 수치인 상대간섭 0.1 이하에서는 오목함수임을 확인하였다. 또한, 제안하는 Convex Optimization 해법은 상대간섭 수치 0.1 이하에서 적용이 가능함을 확인하였다.