• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.1-23
• /
• 2005

The decentralized static output feedback design problem is considered. A constrained trust region method is developed that solves this optimal control problem when a complete set of state variables is not available. The considered problem is interpreted as a non-linear (non-convex) constrained matrix optimization problem. Then, a decentralized constrained trust region method is developed for this problem class exploiting the diagonal structure of the problem and using inexact computations. Finally, numerical results are given for the proposed method.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2004년도 가을 학술발표논문집 Vol.31 No.2 (1)
• /
• pp.697-699
• /
• 2004

Despite many successful spectral clustering algorithm (based on the spectral decomposition of Laplacian(1) or stochastic matrix(2) ) there are several unsolved problems. Most spectral clustering Problems are based on the normalized of algorithm(3) . are close to the classical graph paritioning problem which is NP-hard problem. To get good solution in polynomial time. it needs to establish its convex form by using relaxation. In this paper, we apply a novel optimization technique. semidefinite programming(SDP). to the unsupervised clustering Problem. and present a new multiple Partitioning method. Experimental results confirm that the Proposed method improves the clustering performance. especially in the Problem of being mixed with non-compact clusters compared to the previous multiple spectral clustering methods.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제14권6호
• /
• pp.2686-2708
• /
• 2020

This paper investigates the energy efficiency of energy harvesting (EH) bidirectional cooperative sensor networks, in which the considered system model enables the uplink information transmission from the sensor (SN) to access point (AP) and the energy supply for the amplify-and-forward (AF) relay and SN using power-splitting (PS) or time-switching (TS) protocol. Considering the minimum EH activation constraint and quality of service (QoS) requirement, energy efficiency is maximized by jointly optimizing the resource division ratio and transmission power. To cope with the non-convexity of the optimizations, we propose the low complexity iterative algorithm based on fractional programming and alternative search method (FAS). The key idea of the proposed algorithm first transforms the objective function into the parameterized polynomial subtractive form. Then we decompose the optimization into two convex sub-problems, which can be solved by conventional convex programming. Simulation results validate that the proposed schemes have better output performance and the iterative algorithm has a fast convergence rate.

• 산업경영시스템학회지
• /
• 제15권26호
• /
• pp.67-76
• /
• 1992

변수의 어떤 값들에 대해 도함수를 가질 수 없는 함수를 최적화해야 하는 등. OR 에서는 여러 상황이 존재한다. 이것은 Convex Analysis〔12〕서 이론적인 differential calculus를 근저로 하는 Non-differentiable Optimization 또는 Non-smooth Optimization 을 취급하는 것이 된다. 이러한 종류의 미분이 가능하지 않은 최적화문제는 연속함수를 위한 종래의 최적화법으로는 그 해법자체가 갖고 있는 연속성의 한계를 극복할 수 없다. 따라서, 이러한 문제를 해결하기 위해 Demyanov〔4〕가 제시한 quasi-differental function의 정의와 이들 함수에 따른 몇가지 주요정리들을 언급하고, 그것들을 토대로 Non-differentiable optimization problem의 수치적인 방법을 수행하기 위해 일종의 modified gradient 법을 제시한다. 이를 이용해서 numerical experiment를 위한 방법을 구체화하여, unrestricted non-differentable optimization problem에 적응하여, 그 수치해 결과를 보여서 그 타당성음 검토하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제13권3호
• /
• pp.1325-1344
• /
• 2019

Recently, to satisfy mobile users' increasing data transmission requirement, energy efficiency (EE) resource allocation in distributed antenna systems (DASs) has become a hot topic. In this paper, we aim to maximize EE in DASs subject to constraints of the minimum data rate requirement and the maximum transmission power of distributed antenna units (DAUs) with different density distributions. Virtual cell is defined as DAUs selected by the same user equipment (UE) and the size of virtual cells is dependent on the number of subcarriers and the transmission power. Specifically, the selection rule of DAUs is depended on different scenarios. We develop two scenarios based on the density of DAUs, namely, the sparse scenario and the dense scenario. In the sparse scenario, each DAU can only be selected by one UE to avoid co-channel interference. In order to make the original non-convex optimization problem tractable, we transform it into an equivalent fractional programming and solve by the following two sub-problems: optimal subcarrier allocation to find suitable DAUs; optimal power allocation for each subcarrier. Moreover, in the dense scenario, we consider UEs could access the same channel and generate co-channel interference. The optimization problem could be transformed into a convex form based on interference upper bound and fractional programming. In addition, an energy-efficient DAU selection scheme based on the large scale fading is developed to maximize EE. Finally, simulation results demonstrate the effectiveness of the proposed algorithm for both sparse and dense scenarios.

• Structural Engineering and Mechanics
• /
• 제56권6호
• /
• pp.959-982
• /
• 2015

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
• /
• pp.149-151
• /
• 2007

For several decades, VSC has gained much attention as one of the useful design tools for handling the practical system with uncertainties or disturbances. Generally, the disturbances in the matching condition can be perfectly rejected via VSC; however, these in the mismatching condition are known to be hardly rejected. There have been some trials on it, in which the resulting controls in fact belong to the class of robust control guaranteeing disturbance ${\gamma}$-attenuation. Therefore, in this paper, we propose a new Variable Structure Control (VSC) for a system with mismatched disturbances. The proposed controller is composed of linear and nonlinear parts; the former plays a role in stabilizing the system and the latter takes care of attenuating the disturbances. The main contribution is to introduce the concept of switching-zone, rather than switching-surface, that is designed through piece-wise Lyapunov functions. The resulting non-convex conditions are formulated with an iterative linear programming algorithm, which provides an excellent performance of almost rejecting the disturbances.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제9권3호
• /
• pp.921-940
• /
• 2015

In this paper, we investigate the multi-resource allocation problem, a unique feature of which is that the multiple resources can compensate each other while achieving the desired system performance. In particular, power and time allocations are jointly optimized with the target of energy efficiency under the resource-limited constraints. Different from previous studies on the power-time tradeoff, we consider a multi-server case where the concurrent serving users are quantitatively restricted. Therefore user selection is investigated accompanying the resource allocation, making the power-time tradeoff occur not only between the users in the same server but also in different servers. The complex multivariate optimization problem can be modeled as a variant of 2-Dimension Bin Packing Problem (V2D-BPP), which is a joint non-linear and integer programming problem. Though we use state decomposition model to transform it into a convex optimization problem, the variables are still coupled. Therefore, we propose an Iterative Dual Optimization (IDO) algorithm to obtain its optimal solution. Simulations show that the joint multi-resource allocation algorithm outperforms two existing non-joint algorithms from the perspective of energy efficiency.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제15권6호
• /
• pp.2282-2303
• /
• 2021

To solve the problems of heavy computing load and system transmission pressure in energy internet (EI), we establish a three-tier cloud-edge integrated EI network based on a cloud-edge collaborative computing to achieve the tradeoff between energy consumption and the system delay. A joint optimization problem for resource allocation and task offloading in the threetier cloud-edge integrated EI network is formulated to minimize the total system cost under the constraints of the task scheduling binary variables of each sensor node, the maximum uplink transmit power of each sensor node, the limited computation capability of the sensor node and the maximum computation resource of each edge server, which is a Mixed Integer Non-linear Programming (MINLP) problem. To solve the problem, we propose a joint task offloading and resource allocation algorithm (JTOARA), which is decomposed into three subproblems including the uplink transmission power allocation sub-problem, the computation resource allocation sub-problem, and the offloading scheme selection subproblem. Then, the power allocation of each sensor node is achieved by bisection search algorithm, which has a fast convergence. While the computation resource allocation is derived by line optimization method and convex optimization theory. Finally, to achieve the optimal task offloading, we propose a cloud-edge collaborative computation offloading schemes based on game theory and prove the existence of Nash Equilibrium. The simulation results demonstrate that our proposed algorithm can improve output performance as comparing with the conventional algorithms, and its performance is close to the that of the enumerative algorithm.