• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.10
• /
• pp.4025-4041
• /
• 2020

Mobile edge computing (MEC) is capable of providing services to smart devices nearby through radio access networks and thus improving service experience of users. In this paper, an offloading strategy for the joint optimization of computing and communication resources in multi-user and multi-MEC overlapping scene was proposed. In addition, under the condition that wireless transmission resources and MEC computing resources were limited and task completion delay was within the maximum tolerance time, the optimization problem of minimizing energy consumption of all users was created, which was then further divided into two subproblems, i.e. offloading strategy and resource allocation. These two subproblems were then solved by the game theory and Lagrangian function to obtain the optimal task offloading strategy and resource allocation plan, and the Nash equilibrium of user offloading strategy games and convex optimization of resource allocation were proved. The simulation results showed that the proposed algorithm could effectively reduce the energy consumption of users.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2004.10a
• /
• pp.250-278
• /
• 2004

The product rate variation problem, to be called the PRVP, is to sequence different type units that minimizes the maximum value of a deviation function between ideal and actual rates. The PRVP is an important scheduling problem that arises on mixed-model assembly lines. A surge of research has examined very interesting methods for the PRVP. We believe, however, that several issues are still open with respect to this problem. In this study, we consider convex bipartite graphs, perfect matchings, permanents and balanced sequences. The ultimate objective of this study is to show that we can provide a more efficient and in-depth procedure with a graph theoretic approach in order to solve the PRVP. To achieve this goal, we propose formal alternative proofs for some of the results stated in the previous studies, and establish several new results.

• ETRI Journal
• /
• v.24 no.3
• /
• pp.239-246
• /
• 2002

We investigate an alternative blind adaptive multiuser detection scheme based on a non-canonical linearly constrained constant modulus (LCCM) criterion and prove that, under the constrained condition, the non-canonical linearly constrained constant modulus algorithm (LCCMA) can completely remove multiple -access interference. We further demonstrate that the non-canonical LCCM criterion function is strictly convex in the noise-free state, and that under the constrained condition, it is also strictly convex even where small noise is present. We present a simple method for selecting the constant as well as a stochastic gradient algorithm for implementing our scheme. Numerical simulation results verify the scheme's efficiency.

• ICROS
• /
• v.10 no.3
• /
• pp.27-33
• /
• 2004

최적화는 시스템공학에서 자주 등장하는 문제이며 흔히 다음과 같은 수학적 계획(mathematical programming) 문제로 표현된다. min f(x) (P) subject to g(x) ≤ 0 h(x) ： 0 여기서 x∈R/sup n/, f：R/sup n/→R, g：R/sup n/→R/sup l/, h：R/sup n/→R/sup m/, 그리고 n m이다. 만약 목적함수(objective function)와 가능 영역(feasible region)이 볼록(convex)하다면, 예를 틀어 f(x)와 g(x)가 아래로 볼록하고 h(x)가 선형이라면. 이는 볼록 문제(convex problem)이며 오직 하나의 지역 최소점(local minimum)을 가진다. 그러나 많은 경우. 예를 들어 h(x)가 비선형이라면, 여러 개의 지역 최소점을 가질 수 있는 비 볼록 문제(nonconvex problem)가 된다. 이때 진정한 최소점을 찾는 것. 즉 전역 최적화 (global optimization)가 요구된다.(중략)

• Journal of the Chungcheong Mathematical Society
• /
• v.1 no.1
• /
• pp.71-76
• /
• 1988

For each continuous convex function ${\phi}$ defined on an open convex subset $A_{\phi}$ of a Banach space X, if we define a positively homogeneous sublinear functional ${\sigma}_x$ on X by ${\sigma}_x(y)=\sup{\lbrace}f(y)\;:\;f{\in}{\partial}{\phi}(x){\rbrace}$, where ${\partial}{\phi}(x)$ is a subdifferential of ${\phi}$ at x, then we get the following characterization theorem of Gateaux differentiability (weak Asplund) sapce. THEOREM. For every ${\phi}$ above, $D_{\phi}={\lbrace}x{\in}A\;:\;\sup_{||u||=1}\;{\sigma}_x(u)+{\sigma}_x(-u)=0{\rbrace}$ contains dense (dense $G_{\delta}$) subset of $A_{\phi}$ if and only if X is a Gateaux differentiability (weak Asplund) space.

• Journal of Institute of Control, Robotics and Systems
• /
• v.11 no.4
• /
• pp.279-283
• /
• 2005

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.

• Journal of the Korean Society of Safety
• /
• v.26 no.4
• /
• pp.80-86
• /
• 2011

Structural optimization algorithm of steel box girder bridges using improved higher-order approximate reanalysis technique is proposed in this paper. The proposed approximation method is a generalization of the convex approximation method. The order of the approximate reanalysis for each function is analytically adjusted in the optimization process. This self-adjusted capability makes the approximate structural analysis values conservative enough to maintain the optimum design point of the approximate problem. The efficiency of proposed optimazation algorithm, compared with conventional algorithm, is successfully demonstrated in the steel box girder bridges. The efficiency and robustness of proposed algorithm is also demonstrated in practical steel box girder bridges.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.441-452
• /
• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.401-430
• /
• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.395-408
• /
• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.