Готові списки джерел за темами / Mixed-integer quadratic program

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Добірка наукової літератури з теми "Mixed-integer quadratic program"

Автор: Grafiati

Опубліковано: 8 березня 2025

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Статті в журналах з теми "Mixed-integer quadratic program"

Gondzio, Jacek, and E. Alper Yıldırım. "Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations." Journal of Global Optimization 81, no. 2 (April 20, 2021): 293–321. http://dx.doi.org/10.1007/s10898-021-01017-y.

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AbstractA standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

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Kimura, Keiji, Hayato Waki, and Masaya Yasuda. "Application of mixed integer quadratic program to shortest vector problems." JSIAM Letters 9 (2017): 65–68. http://dx.doi.org/10.14495/jsiaml.9.65.

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Chen, Zhiping, and Zongben Xu. "Continuity and Stability of a Quadratic Mixed-Integer Stochastic Program." Numerical Functional Analysis and Optimization 30, no. 5-6 (June 30, 2009): 462–77. http://dx.doi.org/10.1080/01630560902920668.

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Zhao, Yingfeng, and Sanyang Liu. "Global optimization algorithm for mixed integer quadratically constrained quadratic program." Journal of Computational and Applied Mathematics 319 (August 2017): 159–69. http://dx.doi.org/10.1016/j.cam.2016.12.037.

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Feitelberg, Jacob, Amitabh Basu, and Tamás Budavári. "Fast Globally Optimal Catalog Matching using MIQCP." Astronomical Journal 166, no. 4 (September 27, 2023): 174. http://dx.doi.org/10.3847/1538-3881/acf5e2.

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Abstract We propose a novel exact method to solve the probabilistic catalog matching problem faster than previously possible. Our new approach uses mixed integer programming and introduces quadratic constraints to shrink the problem by multiple orders of magnitude. We also provide a method to use a feasible solution to dramatically speed up our algorithm. This gain in performance is dependent on how close to optimal the feasible solution is. Also, we are able to provide good solutions by stopping our mixed integer programming solver early. Using simulated catalogs, we empirically show that our new mixed integer program with quadratic constraints is able to be set up and solved much faster than previous large linear formulations. We also demonstrate our new approach on real-world data from the Hubble Source Catalog. This paper is accompanied by publicly available software to demonstrate the proposed method.

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Cvokic, Dimitrije. "A leader-follower single allocation hub location problem under fixed markups." Filomat 34, no. 8 (2020): 2463–84. http://dx.doi.org/10.2298/fil2008463c.

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This study examines a scenario in which two competitors, called a leader and a follower, sequentially create their hub and spoke networks to maximize their profits. It is assumed that a non-hub node can be allocated to at most one hub. The pricing is regulated with a fixed markup. Demand is split according to the logit model, and customers patronize their choice of route by a price. Two variants of this Stackelberg competition are addressed: deterministic and robust. In both cases, it was shown how to present the problem as a bi-level mixed-integer non-linear program. When it comes to the deterministic variant, a mixed-integer linear reformulation of the follower?s model is given. For the robust variant, it is shown how to reformulate the follower?s program as a mixed-integer conic-quadratic one. The benefits of these reformulations are that they allow the usage of state-of-the-art solvers in finding feasible solutions. As a solution approach for the leader, an alternating heuristic is proposed. Computational experiments are conducted on the set of Cinstances and thoroughly discussed, providing some managerial insights.

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Popkov, Alexander S. "Optimal program control in the class of quadratic splines for linear systems." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 4 (2020): 462–70. http://dx.doi.org/10.21638/11701/spbu10.2020.411.

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This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. There is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The solution algorithm consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved by using well-known optimization methods that utilize special software.

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Sadeghian, Omid, Arash Moradzadeh, Behnam Mohammadi-Ivatloo, Mehdi Abapour, and Fausto Pedro Garcia Marquez. "Generation Units Maintenance in Combined Heat and Power Integrated Systems Using the Mixed Integer Quadratic Programming Approach." Energies 13, no. 11 (June 3, 2020): 2840. http://dx.doi.org/10.3390/en13112840.

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Yearly generation maintenance scheduling (GMS) of generation units is important in each system such as combined heat and power (CHP)-based systems to decrease sudden failures and premature degradation of units. Imposing repair costs and reliability deterioration of system are the consequences of ignoring the GMS program. In this regard, this research accomplishes GMS inside CHP-based systems in order to determine the optimal intervals for predetermined maintenance required duration of CHPs and other units. In this paper, cost minimization is targeted, and violation of units’ technical constraints like feasible operation region of CHPs and power/heat demand balances are avoided by considering related constraints. Demand-response-based short-term generation scheduling is accomplished in this paper considering the maintenance intervals obtained in the long-term plan. Numerical simulation is performed and discussed in detail to evaluate the application of the suggested mixed-integer quadratic programming model that implemented in the General Algebraic Modeling System software package for optimization. Numerical simulation is performed to justify the model effectiveness. The results reveal that long-term maintenance scheduling considerably impacts short-term generation scheduling and total operation cost. Additionally, it is found that the demand response is effective from the cost perspective and changes the generation schedule.

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Yaakob, Shamshul Bahar, Mohd Zamri Hasan, and Amran Ahmed. "Structural Learning of Boltzmann Machine and its Application." Applied Mechanics and Materials 785 (August 2015): 63–67. http://dx.doi.org/10.4028/www.scientific.net/amm.785.63.

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This study proposed a way to solve problem efficiently which is through structural learning of Boltzmann machine. This method used mixed integer quadratic programming to solve the problem. An analysis is conducted by using the ideas of the reliability and risks of units assessed using a variance-covariance matrix and the effect and expanses of replacement are determined. In this study, the mean-variance analysis is formulated as a mathematical program with two objectives: (1) minimization of risk and (2) maximization of expected return. Lastly, the effectiveness of proposed method is illustrated by way of a life cycle management example. The result of this suggested method was demonstrated at the end. By using this method, more effective selection of results is gathered. Thus, this prove that the effectiveness of the decision making process can be reinforced.

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Sterle, Arnold, Christian A. Hans, and Jörg Raisch. "Model predictive control of wakes for wind farm power tracking." Journal of Physics: Conference Series 2767, no. 3 (June 1, 2024): 032005. http://dx.doi.org/10.1088/1742-6596/2767/3/032005.

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Abstract In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows the tracking of a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows the estimation of the rotor effective wind speeds at downstream turbines, based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

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Більше джерел

Дисертації з теми "Mixed-integer quadratic program"

Karnib, Nour. "Application of Optimization in Regional Distribution Network Reconfiguration." Electronic Thesis or Diss., Chasseneuil-du-Poitou, Ecole nationale supérieure de mécanique et d'aérotechnique, 2025. http://www.theses.fr/2025ESMA0001.

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Dans le domaine de la recherche opérationnelle, le sujet de cette thèse consiste à optimiser les réseaux électriques (en particulier les réseaux de distribution) en termes de pertes de puissance. Le principal problème abordé est le problème de la reconfiguration des réseaux de distribution (DNR) et plusieurs variations de ce problème. Le problème DNR est largement étudié dans la littérature et constitue une approche efficace pour les gestionnaires de réseaux de distribution (DSO) afin d’optimiser leurs réseaux en termes de perte de puissance due à la chaleur Joule. Avec la forte intégration de la production distribuée(production décentralisée), la reconfiguration du schéma d’exploitation du réseau devient cruciale pour améliorer l’économie de ces GRD. Le modèle d’optimisation consiste en un problème de programmation quadratique en nombres entiers mixtes (MIQP), où le réseau de distribution est représenté sous la forme d’un graphe, qui sert d’entrée à ce MIQP. Les variables binaires sont l’état de chaque interrupteur (1 ou 0)et les variables continues représentent les flux dans chaque ligne. La fonction objective est la somme des pertes de puissance pour la configuration sélectionnée par le solveur. Cette thèse réduit d’abord le temps de calcul du solveur lorsque les charges et les générations considérées sont statiques (à un seul moment dans le temps). Elle propose une méthode de réduction du réseau, où le graphe d’entrée du MIQP est réduit pour diminuer l’espace de recherche de la solution pour le solveur. Dans le même but, une méthode d’élimination des commutateurs à faible impact est proposée et testée sur un réseau d’agences SRD. Cette méthode consiste à proposer un ensemble de points de fonctionnement pour les coefficients de charge et de production sur l’ensemble du réseau, où le MIQP est lancé de manière séquentielle. Ensuite, les commutateurs à faible impact dans le MIQP sont fixés en tant que données, tandis que les commutateurs les plus importants restent en tant que variables. Les résultats ont montré que la méthode proposée améliorait considérablement le temps de calcul, le rendant environ 177 fois plus rapide dans le cas d’un point de fonctionnement donné indépendant des points initiaux. Après ces tentatives de réduction du temps de calcul du solveur dans le cas statique, une généralisation est proposée, où l’objectif est d’optimiser les pertes de puissance sur un horizon temporel. On parle alors de reconfiguration multiple sous contraintes opérationnelles. Ensuite, le cas des reconfigurations libres est exploré, lorsqu’aucune contrainte opérationnelle n’est imposée. Ce cas permet au solveur de modifier la solution à chaque point dans le temps, mais cette approche se heurte à de nombreux obstacles technologiques et économiques. Enfin, dans le cas d’une forte intégration de la production, qu’aucune solution ne peut gérer, la réduction de la puissance est introduite pour réduire la puissance excédentaire et maintenir une solution réalisable
In the domain of operations research, this thesis’s subject consists of optimizing electrical networks (specifically, distribution networks) in terms of power losses. The main adressed problem is the Distribution Network Reconfiguration (DNR) problem and several variations of the problem. The DNR problem is widely studied in the literature and is an effective approach for Distribution System Operators (DSOs) to optimize their networks in terms of power loss due to Joule heat. With the high integration of distributed generation (decentralized generation), reconfiguring the network’s operation scheme becomes crucial to improving the economics for these DSOs. The optimization model consists of a Mixed Integer Quadratic Programming (MIQP) problem, where the distribution network is represented as a graph, which serves as an input for this MIQP. The binary variables consist of the state of each switch (1 or 0) along with the continuous variables representing the flows in each line. The objective function is the sum of power losses for the configuration selected by the solver. This thesis first reduces the solver’s computational time when the considered loads and generations are static (at one single point in time). It proposes a network reduction method, where the input graph in the MIQP is reduced to decrease the solution’s search space for the solver. With the same goal, a method for eliminating low-impact switches is proposed and tested on an SRD agency network. This method involves proposing a set of operating points for load and generation coefficients across the entire network, where the MIQP is launched sequentially. Then,the low-impact switches in the MIQP are fixed as data, while the most impactful switches remain as variables. The results showed that the proposed method greatly improved computational time, making it roughly 177 times faster in the case of a given operating point independent of the initial ones. After these attempts to reduce the solver’s computational time in the static case, a generalization is proposed, where the goal is to optimize power losses over a time horizon. This is referred to as multiple reconfiguration under operational constraints. Then, the case of free reconfigurations is explored, where no operational constraints are imposed. This case allows the solver to change the solution at each time point, but this approach faces many technological and economic barriers. Finally, in the case of high production integration, where no solution can handle it, power curtailment is introduced to curtail power in excess and maintain a feasible solution

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Adams, Warren Philip. "The mixed-integer bilinear programming problem with extensions to zero-one quadratic programs." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/74711.

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This research effort is concerned with a class of mathematical programming problems referred to as Mixed-Integer Bilinear Programming Problems. This class of problems, which arises in production, location-allocation, and distribution-application contexts, may be considered as a discrete version of the well-known Bilinear Programming Problem in that one set of decision variables is restricted to be binary valued. The structure of this problem is studied, and special cases wherein it is readily solvable are identified. For the more general case, a new linearization technique is introduced and demonstrated to lead to a tighter linear programming relaxation than obtained through available linearization methods. Based on this linearization, a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm is developed. Extensive computational experience is provided to test the efficiency of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm. The solution strategy developed for the Mixed-Integer Bilinear Programming Problem may be applied, with suitable modifications,. to other classes of mathematical programming problems: in particular, to the Zero-One Quadratic Programming Problem. In what may be considered as an extension to the work performed on the Mixed-Integer Bilinear Programming Problem, a solution strategy based on an equivalent linear reformulation is developed for the Zero-One Quadratic Programming Problem. The strategy is essentially an implicit enumeration algorithm which employs Lagrangian relaxation, Benders' cutting planes, and local explorations. Computational experience for this problem class is provided to justify the worth of the proposed linear reformulation and algorithm.
Ph. D.

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Lazare, Arnaud. "Global optimization of polynomial programs with mixed-integer variables." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLY011.

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Dans cette thèse, nous nous intéressons à l'étude des programmes polynomiaux, c'est à dire les problème d'optimisation dont la fonction objectif et/ou les contraintes font intervenir des polynômes de plusieurs variables. Ces problèmes ont de nombreuses applications pratiques et constituent actuellement un champ de recherche très actif. Différentes méthodes permettent de les résoudre de façon exacte ou approchée, en utilisant par exemple des relaxationssemidéfinies positives du type "moments-somme de carrés". Mais ces problèmes restent très difficiles et on ne sait résoudre en toute généralité que des instances de petite taille.Dans le cas quadratique, une approche de résolution exacte efficace a été initialement proposée à travers la méthode QCR. Elle se base sur une reformulation quadratique convexe "optimale" au sens de la borne par relaxation continue.Une des motivations de cette thèse est de généraliser cette approche pour le cas des problèmes polynomiaux. Dans la majeure partie de ce manuscrit, nous étudions les problèmes d'optimisation en variables binaires. Nous proposons deux familles de reformulations convexes pour ces problèmes: des reformulations "directes" et des reformulations passant par la quadratisation.Pour les reformulations directes, nous nous intéressons tout d'abord aux linéarisations. Nous introduisons le concept de q-linéarisation, une linéarisation utilisant q variables additionnelles, et comparons les bornes obtenues par relaxation continue pour différentes valeurs de q. Ensuite, nous appliquons la reformulation convexe au problème polynomial, en ajoutant des termes supplémentaires à la fonction objectif, mais sans ajouter de variables ou de contraintes additionnelles.La deuxième famille de reformulations convexes vise à étendre la reformulation quadratique convexe au cas polynomial. Nous proposons plusieurs nouvelles reformulations alternatives que nous comparons aux méthodes existantes sur des instances de la littérature. En particulier nous présentons l'algorithme PQCR pour résoudre des problèmes polynomiaux binaires sans contrainte. La méthode PQCR permet de résoudre des instances jusqu'ici non résolues. En plus des expérimentations numériques, nous proposons aussi une étude théorique visant à comparer les différentes reformulations quadratiques de la littérature puis à leur appliquer une reformulation convexe.Enfin nous considérons des cas plus généraux et nous proposons une méthode permettant de calculer des relaxations convexes pour des problèmes continus
In this thesis, we are interested in the study of polynomial programs, that is optimization problems for which the objective function and/or the constraints are expressed by multivariate polynomials. These problems have many practical applications and are currently actively studied. Different methods can be used to find either a global or a heuristic solution, using for instance, positive semi-definite relaxations as in the "Moment/Sum of squares" method. But these problems remain very difficult and only small instances are addressed. In the quadratic case, an effective exact solution approach was initially proposed in the QCR method. It is based on a quadratic convex reformulation, which is optimal in terms of continuous relaxation bound.One of the motivations of this thesis is to generalize this approach to the case of polynomial programs. In most of this manuscript, we study optimization problems with binary variables. We propose two families of convex reformulations for these problems: "direct" reformulations and quadratic ones.For direct reformulations, we first focus on linearizations. We introduce the concept of q-linearization, that is a linearization using q additional variables, and we compare the bounds obtained by continuous relaxation for different values of q. Then, we apply convex reformulation to the polynomial problem, by adding additional terms to the objective function, but without adding additional variables or constraints.The second family of convex reformulations aims at extending quadratic convex reformulation to the polynomial case. We propose several new alternative reformulations that we compare to existing methods on instances of the literature. In particular we present the algorithm PQCR to solve unconstrained binary polynomial problems. The PQCR method is able to solve several unsolved instances. In addition to numerical experiments, we also propose a theoretical study to compare the different quadratic reformulations of the literature and then apply a convex reformulation to them.Finally, we consider more general problems and we propose a method to compute convex relaxations for continuous problems

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Частини книг з теми "Mixed-integer quadratic program"

Ibanez, Aurelien, Philippe Bidaud, and Vincent Padois. "Automatic Optimal Biped Walking as a Mixed-Integer Quadratic Program." In Advances in Robot Kinematics, 505–16. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06698-1_52.

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Hager, Lukas, and Tobias Kuen. "Optimization of Underground Train Systems." In Unlocking Artificial Intelligence, 303–19. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-64832-8_16.

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AbstractThis chapter presents two approaches for enhancing the sustainability and efficiency of underground train systems. The first approach focuses on the optimization of DC railway power systems, employing a novel Mixed-Integer Quadratically Constrained Quadratic Program (MIQCQP) to control substation feed-in voltages effectively. By minimizing energy losses, this optimization approach demonstrates substantial potential for cost and emission reduction, contributing to a more energy-efficient underground train network. Validation results confirm the accuracy of the proposed model, and realistic instances reveal significant energy savings. The second approach deals with energy-efficient timetabling, a critical aspect in reducing the environmental impact of railway operations. The presented approach seeks to minimize energy consumption through the implementation of two key strategies: promoting energy-efficient driving patterns and optimizing recuperated energy from braking. Leveraging operational data, including power consumption profiles and travel time distributions, the optimization methods demonstrate remarkable potential in reducing energy consumption, subsequently leading to lower electricity costs and environmental benefits. This chapter is largely based on previous work of Hager and Koop on optimization of DC railway power systems and of Bärmann et al. [1] on energy-efficient timetabling.

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Qualizza, Andrea, Pietro Belotti, and François Margot. "Linear Programming Relaxations of Quadratically Constrained Quadratic Programs." In Mixed Integer Nonlinear Programming, 407–26. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1927-3_14.

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Wu, Baiyi, and Rujun Jiang. "Quadratic Convex Reformulations for Integer and Mixed-Integer Quadratic Programs." In International Series in Operations Research & Management Science, 43–58. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53518-0_4.

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Karia, Tanuj, Claire S. Adjiman, and Benoît Chachuat. "Global Optimization of Mixed-Integer Polynomial Programs via Quadratic Reformulation." In 31st European Symposium on Computer Aided Process Engineering, 655–61. Elsevier, 2021. http://dx.doi.org/10.1016/b978-0-323-88506-5.50104-2.

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Тези доповідей конференцій з теми "Mixed-integer quadratic program"

Shen, Daniel, and Marija Ilic. "A Mixed Integer Quadratic Program for Valuing the Impact of Price and Forecast Uncertainty for Wind Generators." In 2024 IEEE Power & Energy Society General Meeting (PESGM), 1–5. IEEE, 2024. http://dx.doi.org/10.1109/pesgm51994.2024.10689191.

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Iftakher, Ashfaq, and M. M. Faruque Hasan. "Exploring Quantum Optimization for Computer-aided Molecular and Process Design." In Foundations of Computer-Aided Process Design, 292–99. Hamilton, Canada: PSE Press, 2024. http://dx.doi.org/10.69997/sct.143809.

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Computer-aided Molecular and Process Design (CAMPD) is an equation-oriented multi-scale decision making framework for designing both materials (molecules) and processes for separation, reaction, and reactive separation whenever material choice significantly impacts process performance. The inherent nonlinearity and nonconvexity in CAMPD optimization models, introduced through the property and process models, pose challenges to state-of-the-art solvers. Recently, quantum computing (QC) has shown promise for solving complex optimization problems, especially those involving discrete decisions. This motivates us to explore the potential usage of quantum optimization techniques for solving CAMPD problems. We have developed a technique for directly solving a class of mixed integer nonlinear programs using QC. Our approach represents both continuous and integer design decisions by a set of binary variables through encoding schemes. This transformation allows to reformulate certain types of CAMPD problems into Quadratic Unconstrained Binary Optimization (QUBO) models that can be directly solved using quantum annealing techniques. We illustrate this technique for the selection of optimal ionic liquids (IL) and the configuration of a reactor-separator process network. We also discuss several challenges that are associated with quantum optimization when solving large scale CAMPD problems.

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Mellinger, Daniel, Alex Kushleyev, and Vijay Kumar. "Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams." In 2012 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2012. http://dx.doi.org/10.1109/icra.2012.6225009.

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Morfin-Magana, Rodrigo, Jesus Rico-Melgoza, Fernando Ornelas-Tellez, Francesco Vasca, and David Cortes-Vega. "Mixed-Integer Quadratic Program for Predictive Control of a Grid-Connected Power Converter." In 2019 IEEE 4th Colombian Conference on Automatic Control (CCAC). IEEE, 2019. http://dx.doi.org/10.1109/ccac.2019.8921107.

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Tang, Sarah, and Vijay Kumar. "Mixed Integer Quadratic Program trajectory generation for a quadrotor with a cable-suspended payload." In 2015 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2015. http://dx.doi.org/10.1109/icra.2015.7139492.

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Dollar, R. Austin, and Ardalan Vahidi. "Predictively Coordinated Vehicle Acceleration and Lane Selection Using Mixed Integer Programming." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9177.

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Autonomous vehicle technology provides the means to optimize motion planning beyond human capacity. In particular, the problem of navigating multi-lane traffic optimally for trip time, energy efficiency, and collision avoidance presents challenges beyond those of single-lane roadways. For example, the host vehicle must simultaneously track multiple obstacles, the drivable region is non-convex, and automated vehicles must obey social expectations. Furthermore, reactive decision-making may result in becoming stuck in an undesirable traffic position. This paper presents a fundamental approach to these problems using model predictive control with a mixed integer quadratic program at its core. Lateral and longitudinal movements are coordinated to avoid collisions, track a velocity and lane, and minimize acceleration. Vehicle-to-vehicle connectivity provides a preview of surrounding vehicles’ motion. Simulation results show a 79% reduction in congestion-induced travel time and an 80% decrease in congestion-induced fuel consumption compared to a rule-based approach.

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Almer, S., S. Mariethoz, and M. Morari. "Real-time solution of mixed-integer quadratic programs for hybrid control of power converters." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6425931.

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Almer, Stefan, Sebastien Mariethoz, and Manfred Morari. "Necessary and sufficient conditions for quasiconvexity of a class of mixed-integer quadratic programs with applications in hybrid MPC." In 2011 American Control Conference. IEEE, 2011. http://dx.doi.org/10.1109/acc.2011.5991357.

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