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作者： Silva, Mauro Viegas da Universidade Estadual Paulista

Neste trabalho, o modelo matemático do problema de fluxo de potência ótimo básico não linear é analisado e manipulado algebricamente para obter um modelo de programação convexa, do tipo cônico de segunda ordem. O conceito de envelopes convexos é apresentado para tratar a não linearidade e não convexidade da restrição trigonométrica inversa que surge ao escrever o modelo de FPO como um modelo cônico. Aplicando duas proposições apresentadas neste trabalho a restrição trigonométrica é resolvida em um pré-processamento por um solver de otimalidade local, neste caso o KNITRO, que enumera todas as possibilidades dos pontos de KKT para obter os envelopes convexos e tornar o modelo de FPO totalmente convexo. O modelo é implementado no AMPL e é resolvido com solvers de otimalidade global com sistemas testes da literatura, nesta tese usam-se os sistemas testes IEEE 14, 30, 57 e 118 barras. Os resultados obtidos são validados comparando-os com resultados fornecidos pelo Matpower, que é um simulador para FPO. Como contribuição desta tese, o modelo convexo de FPO obtido é utilizado como exemplo de aplicações no problema de despacho ótimo de potência ativa e reativa, considerando competições via programação binível. São apresentados dois modelos biníveis e dois modelos uníveis. O modelo iterativo convexo utiliza-se do modelo proposto de FPO convexo e as não linearidades são convexificadas fazendo uso dos envelopes de McCormick. O conceito de dualidade forte é empregado afim de obter um modelo unível convexo. Os modelos biníveis e uníveis são implementados em AMPL e resolvidos utilizando solvers de otimalidade local e global, utilizando os mesmos sistemas testes IEEE do modelo cônico e ainda acrescentando mais dois sistemas testes, um de 2 barras e outro de 8 barras. Os principais resultados obtidos com os quatro modelos de despacho ótimo de potência ativa e reativa propostos são apresentados e *** this work, the basic nonlinear mathematical model for the optimal power f

关键词： Programação convexa Fluxo de potência ótimo Envelopes de McCormick Programação binível Dualidade convex programming Optimal power flow McCormick envelopes Bilevel programming Duality Tese de doutorado

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A-PRIORI ESTIMATION OF NEWTON TYPE HOMOTOPY METHOD FOR CALCULATING AN OPTIMAL SOLUTION OF convex-OPTIMIZATION PROBLEM

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1995年第10期E78A卷 1339-1344页

作者： MAKINO, M Chuo Univ Tokyo Japan

In this paper a priori estimation method is presented for calculating solution of convex optimization problems (COP) with some equality and/or inequality constraints by so-called Newton type homotopy method. The homotopy method is known as an efficient algorithm which can always calculate solution of nonlinear equations under a certain mild condition. Although, in general, it is difficult to estimate a priori computational complexity of calculating solution by the homotopy method. In the presented papers, a sufficient condition is considered for linear homotopy, under which an upper bound of the complexity can be estimated a priori. For the condition it is seen that Urabe type convergence theorem plays an important role. In this paper, by introducing the results, it is shown that under a certain condition a global minimum of COP can be always calculated, and that computational complexity of the calculation can be a priori estimated. Suitability of the estimation for analysing COP is also discussed.

关键词： HOMOTOPY METHOD convex programming NONLINEAR programming COMPUTATIONAL COMPLEXITY MONOTONE OPERATOR NONLINEAR SYSTEM ANALYSIS

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Strictly convex separable optimization with linear equality constraints and bounded variables

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2018年第2期21卷 261-272页

作者： Stefanov, Stefan M. South West Univ Neofit Rilski Dept Informat Blagoevgrad 2700 Bulgaria

In this paper, minimization problem with a separable strictly convex objective function subject to several linear equality constraints and bounds on the variables (box constraints) is considered. Such problems arise in manufacturing, facility location, resource allocation, engineering and economic applications, etc. A necessary and sufficient condition (characterization) is proved for a feasible solution to be the (unique) optimal solution of the considered problem. Primal-dual analysis of the proposed approach is made. Examples of some important separable strictly convex objective functions for the problem under consideration are presented.

关键词： Separable programming convex programming Necessary and sufficient condition Engineering and economic applications

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The potential of constrained SAR focusing for hyperthermia treatment planning: analysis for the head & neck region

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PHYSICS IN MEDICINE AND BIOLOGY 2019年第1期64卷 015013-015013页

作者： Bellizzi, G. G. Drizdal, T. van Rhoon, G. C. Crocco, L. Isernia, T. Paulides, M. M. Univ Mediterranea Reggio Calabria DIIES Reggio Di Calabria Italy Erasmus MC Radiat Oncol Dept Hyperthermia Unit Rotterdam Netherlands Natl Res Council Italy Inst Electromagnet Sensing Environm IREA CNR Naples Italy Czech Tech Univ Fac Biomed Engn Prague Czech Republic Eindhoven Univ Technol Fac Elect Engn Eindhoven Netherlands

Clinical trials have shown that hyperthermia is a potent adjuvant to conventional cancer treatments, but the temperatures currently achieved in the clinic are still suboptimal. Hyperthermia treatment planning simulations have potential to improve the heating profile of phased-array applicators. An important open challenge is the development of an effective optimization procedure that enables uniform heating of the target region while keeping temperature below a threshold in healthy tissues. In this work, we analyzed the effectiveness and efficiency of a recently proposed optimization approach, i.e. focusing via constrained power optimization (FOCO), using 3D simulations of twelve clinical patient specific models. FOCO performance was compared against a clinically used particle swarm based optimization approach. Evaluation metrics were target coverage at the 25% iso-SAR level, target hotspot quotient, median target temperature (T50) and computational requirements. Our results show that, on average, constrained power focusing performs slightly better than the clinical benchmark (Delta T50 = +0.05 degrees C), but outperforms this clinical benchmark for large target volumes (>40 cm(3), Delta T50 = +0.39 degrees C). In addition, the results are achieved in a shorter time ( - 44%) and are repeatable because the approach is formulated as a convex optimization problem.

关键词： treatment planning constrained optimization convex programming SAR

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Dynamized routing policies for minimizing expected waiting time in a multi-class multi-server system

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COMPUTERS & OPERATIONS RESEARCH 2022年 137卷 105545-105545页

作者： Nourbakhsh, Vahid Turner, John Univ Calif Irvine Paul Merage Sch Business Irvine CA 92697 USA

Minimizing queue waiting time in multi-class multi-server systems, where the service time depends both on the job type and the server type, has wide applications in transportation systems such as emergency networks and taxi networks, service systems such as call centers, and distributed computing platforms. However, the optimal dynamic policy for this problem is not known and remains a hard open problem. In our approach, we develop a math program to model a static variant of this routing problem and use the solution from this math program to construct several novel dynamic policies. In three categories, namely, (i) policies that do not block jobs, (ii) policies that block jobs statically (i.e., blocking jobs using a predetermined blocking probability), and (ii) policies that block jobs dynamically (i.e., blocking jobs when all feasible servers are busy), we compare the performance of our policies with Fastest-Server-First (FSF), a well-known routing policy for such problems in practice and in the literature. Our experiments show that our proposed overflow dynamic routing policies outperform FSF and its extensions, FSFStaticBlock and FSFDynamicBlock. Moreover, to showcase our methodology, we apply our proposed policies to the problem of assigning fire incidents in Irvine, CA, to fire stations.

关键词： Expected queue waiting time Routing policy convex programming Transportation on demand Call center

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Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2021年第1期42卷 1-16页

作者： Stefanov, Stefan M. South West Univ Neofit Rilski Dept Informat Blagoevgrad 2700 Bulgaria

A separable convex continuous knapsack problem with a single equality constraint and bounded variables is considered in this paper. Necessary and sufficient condition (characterization) for a feasible solution to be an optimal solution to this problem is stated, and characterization theorem in terms of a relaxed problem is formulated and proved. Versions of this problem with a single inequality constraint of the form "less than or equal to" and "greater than or equal to" are also considered, and sufficient conditions for solving these problems are stated and proved, based on the characterization theorem for the original problem. Examples of some convex separable objective functions for the considered problems are presented.

关键词： Knapsack problem Separable programming convex programming Optimality conditions

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A Counting-based Approach for Efficient k-Clique Densest Subgraph Discovery

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Proceedings of the ACM on Management of Data 2024年第3期2卷 1-27页

作者： Yingli Zhou Qingshuo Guo Yixiang Fang Chenhao Ma The Chinese University of Hong Kong Shenzhen Shenzhen Guangdong China

Densest subgraph discovery (DSD) is a fundamental topic in graph mining. It has been extensively studied in the literature and has found many real applications in a wide range of fields, such as biology, finance, and social networks. As a typical problem of DSD, the k-clique densest subgraph (CDS) problem aims to detect a subgraph from a graph, such that the ratio of the number of k-cliques over the number of its vertices is maximized. This problem has received plenty of attention in the literature, and is widely used in identifying larger ''near-cliques''. Existing CDS solutions, either k-core or convex programming based solutions, often need to enumerate almost all the k-cliques, which is very inefficient because real-world graphs usually have a vast number of k-cliques. To improve the efficiency, in this paper, we propose a novel framework based on the Frank-Wolfe algorithm, which only needs k-clique counting, rather than k-clique enumeration, where the former one is often much faster than the latter one. Based on the framework, we develop an efficient approximation algorithm, by employing the state-of-the-art k-clique counting algorithm and proposing some optimization techniques. We have performed extensive experimental evaluation on 14 real-world large graphs and the results demonstrate the high efficiency of our algorithms. Particularly, our algorithm is up to seven orders of magnitude faster than the state-of-the-art algorithm with the same accuracy guarantee.

关键词： clique densest subgraph convex programming graph density

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Optimal energy management of residential battery storage under uncertainty

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2021年第2期31卷

作者： Su, Hao Zhou, Yun Feng, Donghan Li, Hengjie Numan, Muhammad Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Dept Elect Engn Shanghai 200240 Peoples R China Minist Educ Key Lab Control Power Transmiss & Convers SJTU Shanghai 200240 Peoples R China Lanzhou Univ Technol Coll Elect & Informat Engn Lanzhou Peoples R China

Backgroud: The uncertainty associated with renewable generation and loads imposes various challenges for the economic operation of microgrids. On the residential side, energy storage systems are implemented with high expectations to enhance photovoltaic power consumption and electricity price arbitrage. Aims: This paper proposes an expectation-oriented stochastic model for optimal energy management of household batteries to cope with the uncertain electricity generation and consumption. Materials & Methods: The exact cost expectation of daily operation is formulated as an alternative to the conventional scenario-based average approximation. A predictive control-based battery scheduling mechanism is developed further to apply the proposed model to intraday energy storage management. Results: Simulation results validate the convexity of the proposed model. Discussion: Although nonlinear in nature, the resultant optimization problem is proven to be convex, which ensures computable global optimal solutions for the proposed model. Conclusion: Simulation results demonstrate the effectiveness of the proposed scheduling strategy compared with existing methods.

关键词： battery energy storage convex programming stochastic optimization uncertainty

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Stochastic programming approach for static origin-destination matrix reconstruction problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 157卷 107373-107373页

作者： Jeong, In-Jae Park, Dongjoo Hanyang Univ Dept Ind Engn Seoul 133791 South Korea Univ Seoul Dept Transportat Engn Seoul South Korea 222 Wangshimniro Seoul 04763 South Korea 163 Seoulsiripdae Ro Seoul 02504 South Korea

We propose a stochastic programming approach for a static origin-destination (OD) reconstruction problem. We focus on the reconstruction of route flows such that the likelihood function of route flows is maximized. The route volumes are assumed to follow exponential families that are known or estimated in advance. The consideration of the joint distribution function of route flows eliminates the route selection from the model, as the route choice patterns are embedded in the distribution of the route flows. We assume that additional information regarding the traffic counts (i.e., node counts, link counts, and turn counts) is available. Finally, solution methodologies for different stochastic programmings are proposed: barrier method and Primal-dual interior point method for Quadratic programming and convex programming respectively. We compared the proposed stochastic models with the entropy approach. Experimental results indicate that the inclusion of traffic-count information in the stochastic model significantly improves the accuracy of OD reconstruction if we can predict the correct distribution of route flows. Meanwhile the entropy approach requires the inclusion of the additional information on the true volumes of route flows to achieve a similar level of performance. We apply the proposed algorithm to the bus transit system of Seoul, Korea using bus-card data. Compared with the real OD volumes, the reconstruction is fairly accurate.

关键词： Barrier method convex programming Exponential family OD estimation

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Partition-based multi-agent optimization in the presence of lossy and asynchronous communication

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AUTOMATICA 2020年 111卷 108648-000页

作者： Todescato, Marco Bof, Nicoletta Cavraro, Guido Carli, Ruggero Schenato, Luca BCAI Renningen Germany NREL Power Syst Engn Ctr Golden CO USA Dept Informat Engn DEI Padua Italy DEI Padua Italy NREL Golden CO USA US DOE Washington DC 20585 USA

We address the problem of multi-agent partition-based convex optimization which arises, for example, in robot localization problems and in regional state estimation in smart grids. More specifically, the global cost function is the sum of locally coupled cost functions that depend only on each agent variables and their neighbors' variables. Inspired by a generalized gradient descent strategy, namely the Block Jacobi iteration, we propose an algorithm amenable to a scalable distributed implementation, i.e., each agent eventually computes only the optimal values for its own variables via local communication with its neighbors. In particular, we provide sufficient conditions for global and semi-global exponential stability for the proposed algorithms even in the presence of lossy communications and asynchronous updates. The theoretical analysis relies on novel tools on Lyapunov theory based on separation of time scales and averaging theory for discrete-time systems. Finally, the proposed algorithm is numerically tested on the IEEE 123 nodes distribution feeder in the context of multi-area robust state estimation of smart grids in the presence of measurement outliers. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： convex programming Generalized gradient Distributed optimization Communication failures

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