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MATHEMATICAL programming 1982年第3期22卷 332-349页

作者： LAZIMY, R The Hebrew University Jerusalem Israel

This paper considers mixed-integer quadratic programs in which the objective function is quadratic in the integer and in the continuous variables, and the constraints are linear in the variables of both types. The generalized Benders' decomposition is a suitable approach for solving such programs. However, the program does not become more tractable if this method is used, since Benders' cuts are quadratic in the integer variables. A new equivalent formulation that renders the program tractable is developed, under which the dual objective function is linear in the integer variables and the dual constraint set is independent of these variables. Benders' cuts that are derived from the new formulation are linear in the integer variables, and the original problem is decomposed into a series of integer linear master problems and standard quadratic subproblems. The new formulation does not introduce new primary variables or new constraints into the computational steps of the decomposition algorithm.

关键词： Generalized Benders Decomposition Generalized Inverses integer Linear Programs mixed-integer quadratic programming quadratic Duality Theory quadratic programming

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mixed-integer quadratic programming approach for noninvasive estimation of respiratory effort profile during pressure support ventilation

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023年第1期39卷 e3668-e3668页

作者： Victor Jr, Marcus H. H. Maximo, Marcos R. O. A. Matsumoto, Monica M. S. Pereira, Sergio M. Tucci, Mauro R. R. Aeronaut Inst Technol Med Elect Devices Lab LabMed Elect Engn Sao Paulo Brazil Univ Sao Paulo Hosp Clin HCFMUSP Fac Med Div PneumolInst Coracao Sao Paulo Brazil Aeronaut Inst Technol Comp Sci Div Autonomous Computat Syst Lab LAB SCA Sao Paulo Brazil St Michaels Hosp Dept Anesthesia & Pain Med Toronto ON Canada Aeronaut Inst Technol Elect Engn Div Vila Acacias 50 BR-12228900 Sao Jose Dos Campos SP Brazil

Information about respiratory mechanics such as resistance, elastance, and muscular pressure is important to mitigate ventilator-induced lung injury. Particularly during pressure support ventilation, the available options to quantify breathing effort and calculate respiratory system mechanics are often invasive or complex. We herein propose a robust and flexible estimation of respiratory effort better than current methods. We developed a method for non-invasively estimating breathing effort using only flow and pressure signals. mixed-integer quadratic programming (MIQP) was employed, and the binary variables were the switching moments of the respiratory effort waveform. Mathematical constraints, based on ventilation physiology, were set for some variables to restrict feasible solutions. Simulated and patient data were used to verify our method, and the results were compared to an established estimation methodology. Our algorithm successfully estimated the respiratory effort, resistance, and elastance of the respiratory system, resulting in more robust performance and faster solver times than a previously proposed algorithm that used quadratic programming (QP) techniques. In a numerical simulation benchmark, the worst-case errors for resistance and elastance were 25% and 23% for QP versus < 0.1% and < 0.1% for MIQP, whose solver times were 4.7 s and 0.5 s, respectively. This approach can estimate several breathing effort profiles and identify the respiratory system's mechanical properties in invasively ventilated critically ill patients.

关键词： mechanical ventilation mixed-integer quadratic programming parameter estimation pressure support ventilation respiratory effort system identification

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mixed-integer quadratic programming Based Rounding Technique for Power System State Estimation with Discrete and Continuous Variables

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2013年第5期41卷 555-567页

作者： Maalouf, H. Jabr, R. A. Awad, M. Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

As a basic energy management system function that processes real-time measurements, state estimation deals with both continuous and discrete variables to estimate states in a power system. One possible source for the discrete parameters is the transformer taps, whose positions should be estimated with high confidence. Given that the tap estimation error causes a network topological modeling inaccuracy, its range should be minimized. Motivated to accurately estimate a state vector including transformer taps, this research presents an estimator based on mixed-integer quadratic programming and a comparison to a recently proposed ordinal optimization formulation based on a sensitivity analysis. Experimental results on the IEEE 30-, 57-, and 118-bus benchmarks reveal a slight superiority of the mixed-integer quadratic programming algorithm in terms of overall accuracy and motivate follow-up research.

关键词： mixed-integer quadratic programming ordinal optimization power system state estimation transformer tap weighted least squares

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Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm

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OPTIMIZATION AND ENGINEERING 2019年第2期20卷 575-603页

作者： Blackburn, Landen Young, Aaron Rogers, Pratt Hedengren, John Powell, Kody Univ Utah Dept Chem Engn Salt Lake City UT 84112 USA Univ Utah Dept Min Engn Salt Lake City UT USA Brigham Young Univ Dept Chem Engn Provo UT 84602 USA

As more renewable energy is integrated into the power grid, it is increasingly important to exploit variable electricity pricing structures to minimize commercial utility costs and enable more intermittent renewables on the grid through proactive management of energy storage. Using data from a large campus district energy system, equipped with centralized chilled water plants and a thermal energy storage tank, a novel technique is proposed to optimize this system in real-time, formulated as a mixed-integer quadratic programming problem. This method, titled quadratic programming Hybrid with Augmented Constraints, is sufficiently fast to be computed in real-time for a district chiller system. This method is compared to both Branch and Bound and a simple logical decision algorithm in both speed and optimality. The proposed method for solving this mixed-integer quadratic programming problem proves very successful at achieving a near-optimal solution when compared to a standard Branch and Bound (BnB) algorithm. Although suboptimal, the proposed algorithm takes 99.96-99.99% less computational time than the standard BnB and computes an answer to within 29.9% of the BnB objective function. When compared to a simple logical decision algorithm, which represents an operator manually controlling the plant, the proposed method is estimated to yield 8.10-33.7% in savings on chiller energy costs. The quadratic programming Hybrid with Augmented Constraints algorithm shows potential for use in a real-time optimization application to exploit variable electricity pricing and significantly reduce the costs of running a chiller plant with thermal energy storage.

关键词： Dynamic optimization Chiller mixed-integer quadratic programming Thermal energy storage

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On approximation algorithms for concave mixed-integer quadratic programming

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MATHEMATICAL programming 2018年第1-2期172卷 3-16页

作者： Del Pia, Alberto Univ Wisconsin Wisconsin Inst Discovery Dept Ind & Syst Engn Madison WI 53706 USA

Concave mixed- integer quadratic programming is the problem of minimizing a concave quadratic polynomial over the mixed- integer points in a polyhedral region. In this work we describe an algorithm that finds an - approximate solution to a concave mixed- integer quadratic programming problem. The running time of the proposed algorithm is polynomial in the size of the problem and in 1/ , provided that the number of integer variables and the number of negative eigenvalues of the objective function are fixed. The running time of the proposed algorithm is expected unless P = NP.

关键词： mixed-integer quadratic programming Approximation algorithms

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Complex portfolio selection via convex mixed-integer quadratic programming: a survey

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2019年第2期26卷 389-414页

作者： Mencarelli, Luca D'Ambrosio, Claudia Ecole Polytech CNRS LIX UMR7161 F-91128 Palaiseau France

In this paper, we review convex mixed-integer quadratic programming approaches to deal with single-objective single-period mean-variance portfolio selection problems under real-world financial constraints. In the first part, after describing the original Markowitz's mean-variance model, we analyze its theoretical and empirical limitations, and summarize the possible improvements by considering robust and probabilistic models, and additional constraints. Moreover, we report some recent theoretical convexity results for the probabilistic portfolio selection problem. In the second part, we overview the exact algorithms proposed to solve the single-objective single-period portfolio selection problem with quadratic risk measure.

关键词： portfolio selection mixed-integer quadratic programming convex MINLP robust and probabilistic optimization exact methods

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Scheduling of head-dependent cascaded hydro systems: mixed-integer quadratic programming approach

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ENERGY CONVERSION AND MANAGEMENT 2010年第3期51卷 524-530页

作者： Catalao, J. P. S. Pousinho, H. M. I. Mendes, V. M. F. Univ Beira Interior Dept Electromech Engn P-6201001 Covilha Portugal Inst Super Engn Lisboa Dept Elect Engn & Automation P-1950062 Lisbon Portugal

This paper is on the problem of short-term hydro, scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Hydro scheduling mixed-integer quadratic programming Head-dependency

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A simple effective heuristic for embedded mixed-integer quadratic programming

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INTERNATIONAL JOURNAL OF CONTROL 2020年第1期93卷 2-12页

作者： Takapoui, Reza Moehle, Nicholas Boyd, Stephen Bemporad, Alberto Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Stanford Univ Dept Elect Engn Informat Syst Lab Stanford CA 94305 USA IMT Inst Adv Studies Lucca Lucca Italy

In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimisation problems. We discuss the favourable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value;indeed, we see that in many cases, it finds the global solution.

关键词： mixed-integer quadratic programming heuristic ADMM embedded applications

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Model complexity reduction of chemical reaction networks using mixed-integer quadratic programming

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2013年第10期65卷 1575-1595页

作者： Hannernann-Tamas, Ralf Gabor, Attila Szederkenyi, Gabor Hangos, Katalin M. Hungarian Acad Sci MTA SZTAKI Comp & Automat Res Inst Proc Control Res Grp H-1111 Budapest Hungary Univ Pannonia Dept Elect Engn & Informat Syst H-8200 Veszprem Hungary Pazmany Peter Catholic Univ Fac Informat Technol H-1083 Budapest Hungary

The model complexity reduction problem of large chemical reaction networks under isobaric and isothermal conditions is considered. With a given detailed kinetic mechanism and measured data of the key species over a finite time horizon, the complexity reduction is formulated in the form of a mixed-integer quadratic optimization problem where the objective function is derived from the parametric sensitivity matrix. The proposed method sequentially eliminates reactions from the mechanism and simultaneously tunes the remaining parameters until the pre-specified tolerance limit in the species concentration space is reached. The computational efficiency and numerical stability of the optimization are improved by a pre-reduction step followed by suitable scaling and initial conditioning of the Hessian involved. The proposed complexity reduction method is illustrated using three well-known case studies taken from reaction kinetics literature. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Chemical reaction networks Model reduction mixed-integer quadratic programming Sensitivity analysis

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A NOTE ON BENDERS DECOMPOSITION IN mixed-integer quadratic-programming

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OPERATIONS RESEARCH LETTERS 1990年第2期9卷 81-83页

作者： FLIPPO, OE KAN, AHGR Econometric Institute Erasmus University Rotterdam P.O. Box 1738 3000 DR Rotterdam The Netherlands

In this note two decomposition methods are improved for mixed-integer quadratic Programs, developed by E. Balas and R. Lazimy.

关键词： Benders decomposition duality mixed-integer quadratic programming

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