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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第1期64卷 101-118页

作者： JEFFERSON, TR WANG, YP SCOTT, CH TEMPLE UNIV DEPT MATHPHILADELPHIAPA 19122 UNIV CALIF IRVINE GRAD SCH MANAGEMENTIRVINECA 92717

geometric programming is based on functions called posynomials, the terms of which are log-linear. This class of programs is extended from the composition of an exponential and a linear function to an exponential and a convex function. The resulting duality theory for composite geometric programs retains many of the qualities of geometric programming duality, while at the same time encompassing new areas of application. As an application, composite geometric programming is applied to exponential geometric programming. A pure dual is developed for the first time and used to solve a problem from the literature.

关键词： geometric programming convex programming exponential geometric programming transcendental geometric programming

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The Set of Optimal Solutions of geometric programming Problem with Max-Product Fuzzy Relational Equations Constraints

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2016年第3期18卷 436-447页

作者： Zhou, Xue-Gang Cao, Bing-Yuan Yang, Xiao-Peng Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Guangdong Peoples R China Guangdong Univ Finance Dept Appl Math Guangzhou 510521 Guangdong Peoples R China Guangzhou Vocat Coll Sci & Technol Guangzhou 510550 Guangdong Peoples R China Hanshan Normal Univ Dept Math & Stat Chaozhou 521041 Guangdong Peoples R China

In this paper, we consider how to get the set of optimal solutions of geometric programming problem with single-term exponents subject to a system of fuzzy relational equations about max-product composition. The feasible domain of this problem is nonconvex. Firstly, we propose some algorithms to illustrate how to get the set of optimal solutions based on three cases. Secondly, we show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of optimal lower solutions. If we know the optimal value, the maximum optimal solution can be easily computed. However, solving all optimal lower solutions remains as a challenging problem, since finding all the potential minimal solutions of max-product fuzzy relational equations is an NP-hard problem. Finally, four numerical examples are provided to illustrate validity of the proposed method.

关键词： Optimal solution set Max-product composition Fuzzy relational equations geometric programming

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Optimization of DC-DC Converters via geometric programming

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MATHEMATICAL PROBLEMS IN ENGINEERING 2011年第1期2011卷 1-19页

作者： Ribes-Mallada, U. Leyva, R. Garces, P. Univ Rovira & Virgili Dept Elect Elect & Automat Engn Tarragona 43007 Spain

The paper presents a new methodology for optimizing the design of DC-DC converters. The magnitudes that we take into account are efficiency, ripples, bandwidth, and RHP zero placement. We apply a geometric programming approach, because the variables are positives and the constraints can be expressed in a posynomial form. This approach has all the advantages of convex optimization. We apply the proposed methodology to a boost converter. The paper also describes the optimum designs of a buck converter and a synchronous buck converter, and the method can be easily extended to other converters. The last example allows us to compare the efficiency and bandwidth between these optimal-designed topologies.

关键词： DIRECT currents CONVERTERS (Electronics) geometric programming OPTIMAL designs (Statistics) MATHEMATICAL programming

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Levelized Cost of Energy-Oriented Modular String Inverter Design Optimization for PV Generation System Using geometric programming

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IEEE ACCESS 2022年 10卷 27561-27578页

作者： Son, Yeongrack Mukherjee, Satyaki Mallik, Rahul Majmunovi'c, Branko Dutta, Soham Johnson, Brian Maksimovic, Dragan Seo, Gab-Su Natl Renewable Energy Lab Power Syst Engn Ctr Golden CO 80401 USA Univ Colorado Dept Elect Comp & Energy Engn Boulder CO 80309 USA Delta Elect Amer Milan M Jovanovid Power Elect Lab Durham NC 27709 USA Univ Washington Dept Elect & Comp Engn Seattle WA 98195 USA

Levelized cost of energy (LCOE) is a commonly used metric to assess the cost-to-benefit ratio over the lifetime of an energy resource, such as photovoltaics (PV);however, power electronics engineers tend to rely on metrics such as efficiency and power density, which do not guarantee lifetime cost optimality. Recent work has shown that an LCOE-focused optimization approach can yield improved system designs, leading to improved lifetime performance with balanced lifetime cost and energy generation. This paper outlines an LCOE optimization framework for PV power electronics that uses geometric programming. The large number of circuit parameters and nonlinear nature of the system equations pose significant barriers. Our approach allows for decoupling the design variables, which, in turn, enables superior computational efficiency and a near-optimal solution. By incorporating the power electronics design process and magnetic loss mechanism into the convex design framework, the optimization engine yields practically implementable parameters for a PV converter that minimizes LCOE. An optimization example for a cascaded modular PV inverter architecture is presented that suggests 3.35% LCOE improvement can be achieved by the new power electronics and the advanced optimization. The proposed optimization framework can be applied to other power generation systems to evaluate the effect of the power electronics design on system lifetime costs and efficiency.

关键词： Costs Optimization Inverters Power conversion Fitting Measurement Renewable energy sources Convex optimization geometric programming levelized cost of energy lifetime energy cost magnetic loss modeling solar inverters modular multilevel converter

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Joint source and relay power allocation in amplify-and-forward relay networks: a unified geometric programming framework

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IET COMMUNICATIONS 2011年第16期5卷 2301-2309页

作者： Fang, W. -H. Deng, M. -J. Chen, Y. -T. Natl Taiwan Univ Sci & Technol Dept Elect Engn Taipei Taiwan

This study presents some joint source and relay power allocation algorithms in the amplify-and-forward (AF) relay networks using the efficacious geometric programming (GP). According to the constraints, approximate expressions of the received signal-to-noise ratio are first obtained. Thereafter, the problems are cast into appropriate GP forms according to the constraints. The power allocated to the source(s) and to the relays is then determined iteratively via the single condensation method. The new GP approach is shown to be applicable to a variety of constraints by using all of the relays for assistance and is amenable to asymmetric channels in both the single-user and multi-user AF relay networks. Conducted simulations show that the proposed power allocation schemes can attain superior performance compared with the previous works under various constraints in miscellaneous scenarios.

关键词： ELECTRIC relays geometric programming ALGORITHMS SIGNAL-to-noise ratio SIMULATION methods & models WIRELESS communication systems

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ON THE COMPUTATIONAL UTILITY OF POSYNOMIAL geometric-programming SOLUTION METHODS

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MATHEMATICAL programming 1982年第2期22卷 163-201页

作者： FATTLER, JE REKLAITIS, GV SIN, YT ROOT, RR RAGSDELL, KM PURDUE UNIV DEPT COMP SCIW LAFAYETTEIN 47907 PURDUE UNIV SCH MECH ENGNW LAFAYETTEIN 47907

Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.

关键词： geometric programming Code Comparisons Numerical Testing Nonlinear programming

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LOWER BOUNDS FOR POLYNOMIALS WITH SIMPLEX NEWTON POLYTOPES BASED ON geometric programming

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SIAM JOURNAL ON OPTIMIZATION 2016年第2期26卷 1128-1146页

作者： Iliman, Sadik de Wolff, Timo Goethe Univ Frankfurt Inst Math FB 12 Postfach 11 19 32 D-60054 Frankfurt Germany Texas A&M Univ Dept Math College Stn TX 77843 USA

In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnegative as well as to have a sum of binomial squares representation. These criteria rely on the coefficients and the support of a polynomial and generalize all previous ones by Lasserre, Ghasemi, Marshall, Fidalgo, and Kovacec to polynomials with arbitrary simplex Newton polytopes. This generalization yields a geometric programming approach for computing lower bounds for polynomials that significantly extends the geometric programming method proposed by Ghasemi and Marshall. Furthermore, it shows that geometric programming is strongly related to nonnegativity certificates based on sums of nonnegative circuit polynomials, which were recently introduced by the authors.

关键词： geometric programming lower bound nonnegative polynomial semidefinite programming simplex sparsity sum of nonnegative circuit polynomials sum of squares

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Design of a compact MOSFET model suitable for geometric programming

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INTERNATIONAL JOURNAL OF ELECTRONICS 2024年

作者： Cabrera, Fabian L. Weber, Tiago O. Univ Fed Santa Catarina Integrated Circuits Lab LCI BR-88040900 Florianopolis SC Brazil Univ Fed Santa Catarina Embedded Syst Grp GSE BR-88040900 Florianopolis SC Brazil Univ Fed Rio Grande do Sul Elect Instrumentat & Artificial Intelligence Lab I Porto Alegre Brazil

The design of analog integrated circuits is a demanding task that involves many constraints and objectives. Also, the transistor models employed must consider high-order physics effects to achieve accurate solutions. geometric programming (GP) allows finding the global minimum in optimisation problems, but requires design equations to be in monomial or posynomial form. This work proposes a simplified model inspired on the Advanced Compact MOSFET model tailored to be used in GP problems. The proposed model considers short-channel effects and it is valid in the saturation region with all inversion levels. The equations are presented, first showing the transistor current-voltage characteristic and then the associated capacitances. The validity of the equations is proven by their capacity to fit to the simulated data, achieving a mean error of 0.4% for the main NMOS characteristic. After that, the optimal design of two basic amplifier stages is performed to demonstrate the model usability with GP. The predicted voltage gain and bandwidth of the designed amplifiers are compared with simulations, presenting mean errors of 24.7% and 31.7%, respectively. These errors are low when viewed from a logarithmic perspective and considering the wide design space covered. As GP optimisation guarantees the global minimum location and does not require the usage of a circuit simulator in the loop, the proposed GP-friendly compact model can enable fast and accurate optimisation of analog integrated circuits.

关键词： Circuit design design methodology geometric programming MOSFET model

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MODULAR DESIGN - AN APPLICATION OF STRUCTURED geometric programming

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OPERATIONS RESEARCH 1970年第3期18卷 441-&页

作者： PASSY, U Technion-Israel Institute of Technology Haifa Israel

This paper considers an efficient algorithm for finding the optimal design of a module under a special set of circumstances that prevail in the design of a module for logistical applications. The method is based on pr... 详细信息

关键词： Algorithms geometric programming Polynomials Mathematical duality Objective functions Mathematical functions Orthogonality Chemical equilibrium Corporations

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Energy efficient routing formation algorithm for hybrid ad-hoc network: A geometric programming approach

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PEER-TO-PEER NETWORKING AND APPLICATIONS 2019年第1期12卷 102-128页

作者： Das, Santosh Kumar Tripathi, Sachin Indian Inst Technol ISM Dept Comp Sci & Engn Dhanbad 826004 Jharkhand India

In this paper, a novel routing formation algorithm called geometric programming based Energy Efficient Routing protocol (GEER) is proposed for hybrid ad-hoc network. It optimizes two sets of objectives: (i) maximize network lifetime and throughput, and (ii) minimize packet loss and routing overhead. The stated optimizations are done by the fusion of multi-objective optimization, geometric programming, and intuitionistic fuzzy set. The combination of stated techniques provides an effective tool that evaluates an optimal solution based on all objectives and estimates non-linear parameters of the network. The proposed method GEER is simulated in LINGO optimization software and validated with some existing methods in several scenarios. The outcomes of validation illustrate that the proposed method GEER outperforms the other existing methods based on several network metrics.

关键词： Hybrid ad-hoc network Multi-objective optimization geometric programming Fuzzy goal Intuitionistic fuzzy set

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