• Title/Summary/Keyword: geometric programming

### MODIFIED GEOMETRIC PROGRAMMING PROBLEM AND ITS APPLICATIONS

• ISLAM SAHIDUL;KUMAR ROY TAPAN
• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.121-144
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• 2005
• In this paper, we propose unconstrained and constrained posynomial Geometric Programming (GP) problem with negative or positive integral degree of difficulty. Conventional GP approach has been modified to solve some special type of GP problems. In specific case, when the degree of difficulty is negative, the normality and the orthogonality conditions of the dual program give a system of linear equations. No general solution vector exists for this system of linear equations. But an approximate solution can be determined by the least square and also max-min method. Here, modified form of geometric programming method has been demonstrated and for that purpose necessary theorems have been derived. Finally, these are illustrated by numerical examples and applications.

### Two-Phase Approach to Optimal Weather Routing Using Real-Time Adaptive A* Algorithm and Geometric Programming (실시간 적응 A* 알고리즘과 기하학 프로그래밍을 이용한 선박 최적항로의 2단계 생성기법 연구)

• Park, Jinmo;Kim, Nakwan
• Journal of Ocean Engineering and Technology
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• v.29 no.3
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• pp.263-269
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• 2015
• This paper proposes a new approach for solving the weather routing problem by dividing it into two phases with the goal of fuel saving. The problem is to decide two optimal variables: the heading angle and speed of the ship under several constraints. In the first phase, the optimal route is obtained using the Real-Time Adaptive A* algorithm with a fixed ship speed. In other words, only the heading angle is decided. The second phase is the speed scheduling phase. In this phase, the original problem, which is a nonlinear optimization problem, is converted into a geometric programming problem. By solving this geometric programming problem, which is a convex optimization problem, we can obtain an optimal speed scheduling solution very efficiently. A simple case of numerical simulation is conducted in order to validate the proposed method, and the results show that the proposed method can save fuel compared to a constant engine output voyage and constant speed voyage.

### Geometric Programming Applied to Multipoint-to-Multipoint MIMO Relay Networks

• Kim, Jaesin;Kim, Suil;Pak, Ui-Young
• Journal of Communications and Networks
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• v.17 no.3
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• pp.241-246
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• 2015
• In this paper, we consider a relaying system which employs a single relay in a wireless network with distributed sources and destinations. Here, all source, destination, and relay nodes are equipped with multiple antennas. For amplify-and-forward relay systems, we confirm the achievable sum rate through a joint multiple source precoders and a single relay filter design. To this end, we propose a new linear processing scheme in terms of maximizing the sum rate performance by applying a blockwise relaying method combined with geometric programming techniques. By allowing the global channel knowledge at the source nodes, we show that this joint design problem is formulated as a standard geometric program, which can guarantees a global optimal value under the modified sum rate criterion. Simulation results show that the proposed blockwise relaying scheme with the joint power allocation method provides substantial sum rate gain compared to the conventional schemes.

### 기하학적(幾何學的) 계획법(計劃法)에 의한 수질관리(水質管理) 최적화(最適化) 모델의 해법(解法)에 관(關)한 연구(硏究)

• Baek, Du-Gwon
• Journal of Korean Society for Quality Management
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• v.5 no.1
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• pp.23-29
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• 1977
• Geometric programming is very useful for the solution of certain nonlinear programming problems in which the objective function and the constraints are posynomial expressions. By solving the dual program, it can be obtained that the solution of the primal program of Geometric programming. And, more efficient solution is to form an Augmented program possessing degree of difficult zero. A regional water-quality management problem may involve a multistage constrained optimization with many decision variables. In this problem, especially, appling that solution to it is also useful. This paper is described that : 1) the efficient solution of a water-quality management model formed by Geometric programming and 2) the algorithm developed to apply easily a real system by modifing and simplifing the solution.

### A Robust Pricing/Lot-sizing Model and A Solution Method Based on Geometric Programming

• Lim, Sung-Mook
• Management Science and Financial Engineering
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• v.14 no.2
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• pp.13-23
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• 2008
• The pricing/lot-sizing problem of determining the robust optimal order quantity and selling price is discussed. The uncertainty of parameters characterized by an ellipsoid is explicitly incorporated into the problem. An approximation scheme is proposed to transform the problem into a geometric program, which can be efficiently and reliably solved using interior-point methods.

### Stability and PSR(Power-Supply Rejection) Models for Design Optimization of Capacitor-less LDO Regulators (회로 최적화를 위한 외부 커패시터가 없는 LDO 레귤레이터의 안정도와 PSR 성능 모델)

• Joo, Soyeon;Kim, Jintae;Kim, SoYoung
• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.26 no.1
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• pp.71-80
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• 2015
• LDO(Low Drop-Out) regulators have become an essential building block in modern PMIC(Power Managment IC) to extend battery life of electronic devices. In this paper, we optimize capacitor-less LDO regulator via Geometric Programming(GP) designed using Dongbu HiTek $0.5{\mu}m$ BCDMOS process. GP-compatible models for stability and PSR of LDO regulators are derived based on monomial formulation of transistor characteristics. Average errors between simulation and the proposed model are 9.3 % and 13.1 %, for phase margin and PSR, respectively. Based on the proposed models, the capacitor-less LDO optimization can be performed by changing the PSR constraint of the design. The GP-compatible performance models developed in this work enables the design automation of capacitor-less LDO regulator for different design target specification.

### NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF A CONCAVE RECEIVER OPERATING CHARACTERISTIC CURVE VIA GEOMETRIC PROGRAMMING

• Lee, Kyeong-Eun;Lim, Johan
• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.523-537
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• 2011
• A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.

### Comparative Analysis of Two EOQ based Inventory Models (EOQ 기반 재고 모델의 비교 분석)

• Jung, Hoon
• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.248-256
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• 2005
• In this paper, we compare two EOQ based inventory models under total cost minimization and profit maximization to investigate the difference in the optimal solutions. First of all, optimal solutions for both models through geometric programming (GP) techniques are found considering production (lot sizing) as well as marketing (pricing) decisions. An investigation of the effects of the changes in the optimal solutions according to varied parameters is performed by studying optimality conditions as well as by performing numerical analysis. We then conduct comparative analysis between the models to show the relationships between the optimal solutions of the models where certain conditions in the cost per unit and the demand per unit time are given. Several interesting economic implications and managerial insights are observed from this analysis.

### Design of CMOS Op Amps Using Adaptive Modeling of Transistor Parameters

• Yu, Sang-Dae
• JSTS:Journal of Semiconductor Technology and Science
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• v.12 no.1
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• pp.75-87
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• 2012
• A design paradigm using sequential geometric programming is presented to accurately design CMOS op amps with BSIM3. It is based on new adaptive modeling of transistor parameters through the operating point simulation. This has low modeling cost as well as great simplicity and high accuracy. The short-channel dc, high-frequency small-signal, and short-channel noise models are used to characterize the physical behavior of submicron devices. For low-power and low-voltage design, this paradigm is extended to op amps operating in the subthreshold region. Since the biasing and modeling errors are less than 0.25%, the characteristics of the op amps well match simulation results. In addition, small dependency of design results on initial values indicates that a designed op amp may be close to the global optimum. Finally, the design paradigm is illustrated by optimizing CMOS op amps with accurate transfer function.

### Design Optimization of CML-Based High-Speed Digital Circuits (전류모드 논리 회로 기반의 고속 디지털 회로 디자인 최적화)

• Jang, Ikchan;Kim, Jintae;Kim, SoYoung
• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.11
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• pp.57-65
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• 2014
• This paper presents a framework that is based on a reconfigurable macro-model of current-mode logic (CML) high-speed digital circuits enabling equation-based design optimization. The proposed macro-model is compatible with geometric programming, thereby enabling constraint-driven top-level power optimization. The proposed optimization framework is applied to a design of CML based serial-link transmitter with user-defined design specifications as an example of high speed digital circuits using 45nm and 90nm CMOS technology. The proposed optimization framework can derive a design with optimal power efficiency for given transistor technology nodes.