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The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期302卷 621-632页

作者： Aparicio, Juan Monge, Juan F. Univ Miguel Hernandez Elche Ctr Operat Res Avda Univ S-N Alicante 03202 Spain

The measurement of technical efficiency is a topic of great interest in microeconomics and engineering. Data Envelopment Analysis (DEA) is one of the existing techniques for measuring technical efficiency. One of the challenges related to DEA is to introduce a "well-defined" efficiency measure. Overall, it means that the technical efficiency measure should satisfy a list of mathematical and economical properties. Regarding this point, an unresolved question in the DEA literature to date, is whether any measure can satisfy both Indication, also called Pareto-efficiency identification, and uniqueness of the projection point generated by the corresponding efficiency optimization model. With this issue in mind, this paper introduces a new family of measures, inspired on the Range-Adjusted Measure (RAM), which satisfy a list of six properties. This family of measures will be called Generalized Range-Adjusted Measure (GRAM). Additionally, we show in this paper how GRAM can be implemented from a computational point of view and we also provide an economical interpretation of its dual program in terms of (shadow) profit maximization. Finally, an empirical example extracted from the literature serves to illustrate the new methodology. (C) 2022 The Author(s). Published by Elsevier B.V.

关键词： Data envelopment analysis Technical efficiency Properties Convex optimization second-order cone programming

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Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming

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Science China Mathematics 2022年第11期65卷 2397-2422页

作者： Liang Chen Junyuan Zhu Xinyuan Zhao School of Mathematics Hunan UniversityChangsha 410082China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics Changsha 410082China School of Mathematics Beijing University of TechnologyBeijing 100124China

In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization ***,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the *** first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity ***,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.

关键词： second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming

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A sequential convex moving horizon estimator for bioprocesses?

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JOURNAL OF PROCESS CONTROL 2022年 116卷 19-24页

作者： Taylor, Josh A. Rapaport, Alain Dochain, Denis Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON Canada Univ Montpellier Inst Agro MISTEA INRAE Montpellier France Catholic Univ Louvain Ottignies Louvain La Neuv Belgium

We design moving horizon state estimators for a general model of bioprocesses. The underlying optimization is nonconvex due to the microbial growth kinetics, which are modeled as nonlinear functions. We relax the nonconvex growth constraints so that the optimization becomes a second-order cone program, which can be solved efficiently at large scales. Unfortunately, solutions to the relaxation can be inexact and thus lead to inaccurate state estimates. To recover feasible, albeit potentially locally optimal solutions, we use the concave-convex procedure, which here takes the form of a sequence of second-order cone programs. We find that the moving horizon state estimators outperform the unscented Kalman filter on numerical examples based on the gradostat and anaerobic digestion when there is high process noise or parameter error. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Moving horizon state estimation second-order cone programming Concave-convex procedure Anaerobic digestion

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Dealing with time in the multiple traveling salespersons problem with moving targets

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2022年第3期30卷 991-1017页

作者： Stieber, Anke Fuegenschuh, Armin Helmut Schmidt Univ Hamburg Germany Brandenburg Univ Technol Cottbus Senftenberg Cottbus Germany

The multiple traveling salespersons problem with moving targets is a generalization of the classical traveling salespersons problem, where the targets (nodes or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salespersons so that each target is reached exactly once within its visibility time window and the sum of all traveled distances of all salespersons is minimal. We present different modeling formulations for this TSP variant. The time requirements are modeled differently in each approach. Our goal is to examine what formulation is most suitable in terms of runtime to solve the multiple traveling salespersons problem with moving targets with exact methods. Computational experiments are carried out on randomly generated test instances to compare the different modeling approaches. The results for large-scale instances show, that the best way to model time requirements is to directly insert them into a formulation with discrete time steps.

关键词： Dynamic traveling salespersons problem Moving targets Time-relaxation Integer linear programming second-order cone programming

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Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF 63

Accurate and Warm-Startable Linear Cutting-Plane Relaxations...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Bienstock, Daniel Villagra, Matias

ISBN: (纸本)9798350316339

We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power FlowProblem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding sharp bounds. Our primary focus concerns the (frequent) case where an ACOPF instance is considered following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence that the cuts computed on the prior instance provide an effective warm-start for our algorithm. © 2024 IEEE.

关键词： second-order cone programming

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Optimal Power Loss Minimization using Static VAR Compensator

Optimal Power Loss Minimization using Static VAR Compensator

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2024 International Conference on Control, Automation and Diagnosis, ICCAD 2024

作者： Haq, Md Nasib Ul Wang, Xin Southern Illinois University Electrical and Computer Engineering EdwardsvilleIL62026 United States Southern Illinois University Edwardsville Electrical and Computer Engineering EdwardsvilleIL62026 United States

ISBN: (纸本)9798350361025

This paper conducts a comparative study on optimizing power loss minimization in electrical power systems by strategically implementing Static VAR Compensator (SVC). The primary focus is on leveraging SVCs to dynamically regulate reactive power, aiming to optimize the overall system operation with the specific goal of minimizing power losses. Through the application of mathematical optimization methodologies, the research aims to identify highly effective deployment strategies for SVCs, ultimately achieving significant reductions in power losses within the network. second-order cone programming (SOCP) based AC Optimal Power Flow (AC OPF) has been used to solve the optimization problem. Static Var Compensator (SVC) is connected to the IEEE 14 bus test power system at different buses to improve voltage profile and minimizing power loss. The findings, obtained through rigorous simulation and analysis, contribute valuable insights into the enhancement of efficiency and performance in power systems. The sensible utilization of SVCs for optimal power loss minimization emerges as a key focal point, encapsulating the primary objectives and outcomes of the study and shedding light on the pursuit of heightened energy efficiency in power systems. © 2024 IEEE.

关键词： second-order cone programming

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Applications of Stochastic Mixed-Integer second-order cone Optimization

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IEEE ACCESS 2022年 10卷 3522-3547页

作者： Alzalg, Baha Alioui, Hadjer Univ Jordan Dept Math Amman 11942 Jordan Ohio State Univ Dept Comp Sci & Engn Columbus OH 43210 USA

second-order cone programming problems are a tractable subclass of convex optimization problems that can be solved using polynomial algorithms. In the last decade, stochastic second-order cone programming problems have been studied, and efficient algorithms for solving them have been developed. The mixed-integer version of these problems is a new class of interest to the optimization community and practitioners, in which certain variables are required to be integers. In this paper, we describe five applications that lead to stochastic mixed-integer second-order cone programming problems. Additionally, we present solution algorithms for solving stochastic mixed-integer second-order cone programming using cuts and relaxations by combining existing algorithms for stochastic second-order cone programming with extensions of mixed-integer second-order cone programming. The applications, which are the focus of this paper, include facility location, portfolio optimization, uncapacitated inventory, battery swapping stations, and berth allocation planning. Considering the fact that mixed-integer programs are usually known to be NP-hard, bringing applications to the surface can detect tractable special cases and inspire for further algorithmic improvements in the future.

关键词： programming Stochastic processes Uncertainty Optimization Convex functions Medical services Licenses second-order cone programming mixed-integer programming stochastic programming applications algorithms

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Optimal dispatching strategy for power and natural gas system in the distribution level with generator using residual differential pressure energy

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ENERGY REPORTS 2022年 8卷 627-633页

作者： Zhao, Yuehao Li, Zhiyi Ju, Ping Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China Hohai Univ Coll Energy & Elect Engn Nanjing 211100 Peoples R China

Natural-gas fired units (NGFU) occupy an increasingly important position in the power system, leading to a closer connection between the power system and natural gas system, especially in the distribution level. To utilize the residual differential pressure energy and reduce operation costs, the conversion model of the generator using residual differential pressure energy is formulated, and then the cooperation model of the power system and natural gas system is built in this paper. Due to the original optimization model of power system and natural gas system in the distribution level is non-convex, the second-order cone programming (SOCP) based on a modified convex concave procedure (CCP) algorithm is used to handle the NP-hard problem. The simulation results show operation costs are reduced via the proposed strategy, and the SOCP based on the modified CCP algorithm achieves good performance in fast solution with the constraint of Weymouth equation. (C) 2021 The Author(s). Published by Elsevier Ltd.

关键词： Power system and natural gas system in the distribution Optimal dispatching strategy generator using residual pressure energy second-order cone programming Modified convex concave procedure

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Minimax Design of M-D Sparse FIR Filters With Arbitrary Frequency Response Using SOCP

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2022年第5期69卷 2403-2407页

作者： Jayaweera, Ashira L. Pakiyarajah, Darukeesan Edussooriya, Chamira U. S. Univ Moratuwa Dept Elect & Telecommun Engn Moratuwa 10400 Sri Lanka Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Jaffna Dept Elect & Elect Engn Killinochchi 44000 Sri Lanka Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA

The number of coefficients of multi-dimensional (M-D) finite-extent impulse response (FIR) filters increases exponentially with the number of dimensions leading to significantly high computational complexities. In this brief, we propose a minimax design method for M-D FIR filters having sparse coefficients, therefore, having low computational complexities. We consider the design of M-D FIR filters with arbitrary frequency responses and low group delays of which the coefficients are complex valued. We formulate the minimax design as a second-order cone programming problem. Design examples confirm that M-D sparse FIR filters designed using the proposed method provide more than 60% reduction in the computational complexity for a similar error in the frequency response approximation compared to M-D FIR nonsparse filters designed using previously proposed minimax methods.

关键词： Finite impulse response filters Design methodology Frequency response Minimization Delays Computational complexity programming Multi-dimensional filters sparse FIR filters low group delay minimax design second-order cone programming

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RPL-SVM: Making SVM Robust Against Missing Values and Partial Labels 20th

RPL-SVM: Making SVM Robust Against Missing Values and Parti...

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20th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2023

作者： Mohandas, Sreenivasan Manwani, Naresh Machine Learning Lab KCIS IIIT Hyderabad Hyderabad India

ISBN: (纸本)9789819970247

With increased data availability, data quality is the biggest problem in using AI models. The data may suffer from missing values and noisy values. Another major challenge is to get accurate labels for feature vectors in the training data. In contrast, in many applications, we can only get weak labels (for example, partial labels, positive-unlabeled data, bandit feedback, etc.). In this paper, we consider uncertainty in both features and labels. More specifically, we assume that feature vectors have missing attributes and are only given partial labels. We present a novel second-order cone programming framework to learn robust classifiers that can tolerate uncertainty in the observations of partially labeled multiclass classification problems. The proposed approach, RPL-SVM, is based on a chance-constrained framework. Experimental results show that RPL-SVM efficiently learns multiclass classifiers with missing values in a partial label setting. This demonstrates the remarkable resilience of RPL-SVM to real-world observational uncertainties. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2024.

关键词： second-order cone programming

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