• Title, Summary, Keyword: minimax

### A NON-COMPACT GENERALIZATION OF HORVATH'S INTERSECTION THEOREM$^*$

• Kim, Won-Kyu
• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.153-162
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• 1995
• Ky Fan's minimax inequality is an important tool in nonlinear functional analysis and its applications, e.g. game theory and economic theory. Since Fan gave his minimax inequality in [2], various extensions of this interesting result have been obtained (see [4,11] and the references therein). Using Fan's minimax inequality, Ha [6] obtained a non-compact version of Sion's minimax theorem in topological vector spaces, and next Geraghty-Lin [3], Granas-Liu [4], Shih-Tan [11], Simons [12], Lin-Quan [10], Park-Bae-Kang [17], Bae-Kim-Tan [1] further generalize Fan's minimax theorem in more general settings. In [9], using the concept of submaximum, Komiya proved a topological minimax theorem which also generalized Sion's minimax theorem and another minimax theorem of Ha in [5] without using linear structures. And next Lin-Quan [10] further generalizes his result to two function versions and non-compact topological settings.

### A Study on the Decision-making of Minimax Facility Location (Minimax에 의한 설비입지의 의사결정에 관한 연구)

• 전만술;이성옥
• Journal of the Society of Korea Industrial and Systems Engineering
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• v.8 no.12
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• pp.1-6
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• 1985
• The purpose of this study is to consider the criteria for decision-making of facility location in view of Minimax. As an illustration of the location of storerooms in a manufacturing plant that minimizes the maximum distance workers must travel to reach a storeroom, the number and variety of location problems that can be formulated appropriately as minimax problems are sizable. A minimax solution can be interpreted as a grease the squeaky wheel solution In solving a minimax location problem, costs other than the maximum cost are not considered.

### GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES

• Kim, Hoon-Joo
• Honam Mathematical Journal
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• v.31 no.4
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• pp.559-578
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• 2009
• In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

### ON THE MINIMAX VARIANCE ESTIMATORS OF SCALE IN TIME TO FAILURE MODELS

• Lee, Jae-Won;Shevlyakov, Georgy-L.
• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.23-31
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• 2002
• A scale parameter is the principal parameter to be estimated, since it corresponds to one of the main reliability characteristics, namely the average time to failure. To provide robustness of scale estimators to gross errors in the data, we apply the Huber minimax approach in time to failure models of the statistical reliability theory. The minimax valiance estimator of scale is obtained in the important particular case of the exponential distribution.

### Minimax Average MSE Designs for Estimating Mean Responses

• Joong-Yang Park
• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.93-101
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• 1996
• The unknown response function is usually approximated by a low order polynomial model. Such an approximation always accompanies bias due to model departure. The minimax Average MSE (AMSE) designs are suggested for estimating mean responses. A class of first order minimax AMSE designs is derived and a specific first order minimax AMSE design is selected from the class by optimizing the secondary criterion related to the power of the lack of fit test.

### A Study on Comparative Evaluation of Application of Software Reliability Model Dependent on Various Hazard Functions (다양한 위험함수에 의존한 소프트웨어 신뢰모형의 적용에 대한 비교 평가에 관한 연구)

• Yang, Tae-Jin
• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.6
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• pp.800-806
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• 2018
• Software efficiency is the probability of failure free use in operating environments, and is the most fundamental factor affecting software system stability. The malfunction of the computer system used in the information technology field may cause a significant loss in the related industry. Therefore, in this study, we analyze the attributes of software reliability models that depend on various hazard functions based on finite fault NHPP model with software failure time data. The hazard function pattern of proposed model is constant for the Goel-Okumoto model, and the Minimax and Rayleigh models follow the incremental pattern, but the hazard function increase value of the Minimax model is smaller than that of the Rayleigh model and the Goel-Okumoto model. Also, the Minimax model was relatively efficient because the true value error of the mean value function m(t) and the mean square error (MSE) of the Minimax model were smaller than those of the Rayleigh and Goel-Okumoto models. The results of this study are expected to be useful for software developers as basic information about the hazard function.

### On the Minimax Disparity Obtaining OWA Operator Weights

• Hong, Dug-Hun
• Journal of Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.273-278
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• 2009
• The determination of the associated weights in the theory of ordered weighted averaging (OWA) operators is one of the important issue. Recently, Wang and Parkan [Information Sciences 175 (2005) 20-29] proposed a minimax disparity approach for obtaining OWA operator weights and the approach is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Liu [International Journal of Approximate Reasoning, accepted] showed that the minimum variance OWA problem of Fuller and Majlender [Fuzzy Sets and Systems 136 (2003) 203-215] and the minimax disparity OWA problem of Wang and Parkan always produce the same weight vector using the dual theory of linear programming. In this paper, we give an improved proof of the minimax disparity problem of Wang and Parkan while Liu's method is rather complicated. Our method gives the exact optimum solution of OWA operator weights for all levels of orness, $0\leq\alpha\leq1$, whose values are piecewise linear and continuous functions of $\alpha$.

### A TWO-FUNCTION MINIMAX THEOREM

• Kim, Won Kyu;Kum, Sangho
• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.321-326
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• 2008
• In this note, using the separation theorem for convex sets, we will give a two functions version generalization of Fan's minimax theorem by relaxing the convexlike assumption to the weak convexlike condition.

### A SIMPLE PROOF OF THE SION MINIMAX THEOREM

• Park, Se-Hie
• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1037-1040
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• 2010
• For convex subsets X of a topological vector space E, we show that a KKM principle implies a Fan-Browder type fixed point theorem and that this theorem implies generalized forms of the Sion minimax theorem.

### QUASI-VARIATIONAL AND MINIMAX INEQUALITIES AND COLLECTIVELY FIXED POINT RESULTS FOR S-KKM MAPS

• O'REGAN DONAL;SHAHZAD NASEER;AGARWAL RAVI P.
• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.739-756
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• 2005
• The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.