• Journal of the Korean Operations Research and Management Science Society
• /
• v.27 no.3
• /
• pp.145-156
• /
• 2002

Business managers are often required to use LP problems to deal with uncertainty inherent in decision making due to rapid changes in today＇s business environments. Uncertain parameters can be easily formulated in the two-stage stochastic LP problems. However, since solution methods are complex and time-consuming, a common approach has been to use modified formulations to provide upper and lower bounds on the two-stage stochastic LP problem. One approach is to use an expected value problem, which provides upper and lower bounds. Another approach is to use “walt-and-see” problem to provide upper and lower bounds. The objective of this paper is to propose a modified approach of “wait-and-see” problem to provide an upper bound and to compare the relative error of optimal value with various upper and lower bounds. A computing experiment is implemented to show the relative error of optimal value with various upper and lower bounds and computing times.

• International Journal of Control, Automation, and Systems
• /
• v.6 no.2
• /
• pp.288-294
• /
• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.323-328
• /
• 2008

In this paper, we introduce some algebraic, rational and polynomial upper bounds of the exponential function on the interval [0,1). And then we compare the acuteness of these bounds.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.33 no.11C
• /
• pp.880-882
• /
• 2008

This paper presents LDPC codes' upper bounds over the waterfall SNR region. The previous researches have focused on the average bound or ensemble bound over the whole SNR region and showed the performance differences for the fixed block size. In this paper, the particular LDPC codes' upper bounds for various block sizes are calculated over the waterfall SNR region and are compared with BP decoding performance. For different block sizes the performance degradation of BP decoding is shown.

• Journal of Communications and Networks
• /
• v.18 no.2
• /
• pp.182-189
• /
• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.477-492
• /
• 1994

For the eigenvalue problem of $Au = \lambda u$ where A is considered as a semi-bounded self-adjoint operator on a Hilbert space, we are used to apply two complentary methods finding upper bounds and lower bounds to the eigenvalues. The most popular method for finding upper bounds may be the Rayleigh-Ritz method which was developed in the 19th century while a method for computing lower bounds may be the method of intermediate eigenvalue problems which has been developed since 1950's. In the method of intermediate eigenvalue problems (IEP), we consider the original operator eigenvalue problem as a perturbation of a simpler, resolvable, self-adjoint eigenvalue problem, called a base problem, that gives rough lower bounds.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.461-469
• /
• 1995

Some bounds for anisotropic torsional rigidity with one plane of elastic symmetry perpendicular to the axis of the beam are derived by making use of the isoperimetric inequalities, complementary variational principles, and the maximum principle. Upper and lower bounds are obtained by applying the isoperimetric inequalities. While the upper bound investigated by the variational principles and maximum principle. The analysis is patterned after the work of Payne and Weinbeger [J. Math. Anal. Appl. 2(1961). pp. 210-216].

• Journal of the Korean Operations Research and Management Science Society
• /
• v.8 no.1
• /
• pp.19-26
• /
• 1983

This paper deals with the problem of locating facilities with upper and lower capacity bounds in a single level physical distribution system at minimum total costs. Several known schemes for location problems with upper capacity bounds only are successfully extended to our case and then implemented into our branch ana bound solution procedure. Computational experiments with twelve test problems suggest the effectiveness of our approach by showing that only a small amount of additional computation is required for our problem as compared to that for the problems with upper capacity bounds.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.425-427
• /
• 1993

Some upper bounds for the solution of the continuous algebraic Riccati equation are presented. These consist of bounds for summations of eigenvalues, products of eigenvalues, individual eigenvalues and the minimum eigenvalue of the solution matrix. Among these bounds, the first three are the first results for the upper bound of each case, while bounds for the minimum eigenvalue supplement the existing ones and require no side conditions for their validities.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.111-121
• /
• 1992

A new method(EVF method) is applied to get lower bounds to frequencies of rotating uniform beams which are clamped or simply supported at one end and free at the other. For the upper bounds, the Rayleigh-Ritz method is employed. Numerical results are presented.