Relevant bibliographies by topics / Quadratically Constrained Linear Programming

Academic literature on the topic 'Quadratically Constrained Linear Programming'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Quadratically Constrained Linear Programming"

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Klomp, M. "Longitudinal force distribution using quadratically constrained linear programming." Vehicle System Dynamics 49, no. 12 (December 2011): 1823–36. http://dx.doi.org/10.1080/00423114.2010.545131.

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Hu, Chenyang, Yuelin Gao, Fuping Tian, and Suxia Ma. "A Relaxed and Bound Algorithm Based on Auxiliary Variables for Quadratically Constrained Quadratic Programming Problem." Mathematics 10, no. 2 (January 16, 2022): 270. http://dx.doi.org/10.3390/math10020270.

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Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality constraints are relaxed, a series of linear relaxation subproblems with auxiliary variables and bound constraints are generated, which can determine the effective lower bound of the global optimal value of QCQP. To enhance the compactness of sub-rectangles and improve the ability to remove sub-rectangles, two rectangle-reduction strategies are employed. Besides, two ϵ-subproblem deletion rules are introduced to improve the convergence speed of the algorithm. Therefore, a relaxation and bound algorithm based on auxiliary variables are proposed to solve QCQP. Numerical experiments show that this algorithm is effective and feasible.
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Alkhalifa, Loay, and Hans Mittelmann. "New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation." Mathematics 10, no. 2 (January 9, 2022): 198. http://dx.doi.org/10.3390/math10020198.

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Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.
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Lara, Hugo José, Abel Soares Siqueira, and Jinyun Yuan. "A Reduced Semidefinite Programming Formulation for HA Assignment Problems in Sport Scheduling." TEMA (São Carlos) 19, no. 3 (December 17, 2018): 471. http://dx.doi.org/10.5540/tema.2018.019.03.471.

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Home-Away Assignment problems are naturally cast as quadraticpro gramming models in binary variables. In this work we compare alternative formulations for this kind of problems. First,write a quadratic programming formulation with linear constraints, and then a quadratically constrained version. We also propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. The quadratic programming formulations leads to semidefinite relaxations, which allows us to approximately solve the models. We compare our SDP relaxation with the MIN-RES-CUT based formulation. Numerical experiments exhibit the characteristics of each model.
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Jain, Pallavi, Gur Saran, and Kamal Srivastava. "A new Integer Linear Programming and Quadratically Constrained Quadratic Programming Formulation for Vertex Bisection Minimization Problem." Journal of Automation, Mobile Robotics & Intelligent Systems 10, no. 1 (February 18, 2016): 69–73. http://dx.doi.org/10.14313/jamris_1-2016/9.

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Fogarty, Colin B., and Dylan S. Small. "Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies Through Quadratically Constrained Linear Programming." Journal of the American Statistical Association 111, no. 516 (October 1, 2016): 1820–30. http://dx.doi.org/10.1080/01621459.2015.1120675.

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Messerer, Florian, Katrin Baumgärtner, and Moritz Diehl. "Survey of sequential convex programming and generalized Gauss-Newton methods." ESAIM: Proceedings and Surveys 71 (August 2021): 64–88. http://dx.doi.org/10.1051/proc/202171107.

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We provide an overview of a class of iterative convex approximation methods for nonlinear optimization problems with convex-over-nonlinear substructure. These problems are characterized by outer convexities on the one hand, and nonlinear, generally nonconvex, but differentiable functions on the other hand. All methods from this class use only first order derivatives of the nonlinear functions and sequentially solve convex optimization problems. All of them are different generalizations of the classical Gauss-Newton (GN) method. We focus on the smooth constrained case and on three methods to address it: Sequential Convex Programming (SCP), Sequential Convex Quadratic Programming (SCQP), and Sequential Quadratically Constrained Quadratic Programming (SQCQP). While the first two methods were previously known, the last is newly proposed and investigated in this paper. We show under mild assumptions that SCP, SCQP and SQCQP have exactly the same local linear convergence – or divergence – rate. We then discuss the special case in which the solution is fully determined by the active constraints, and show that for this case the KKT conditions are sufficient for local optimality and that SCP, SCQP and SQCQP even converge quadratically. In the context of parameter estimation with symmetric convex loss functions, the possible divergence of the methods can in fact be an advantage that helps them to avoid some undesirable local minima: generalizing existing results, we show that the presented methods converge to a local minimum if and only if this local minimum is stable against a mirroring operation applied to the measurement data of the estimation problem. All results are illustrated by numerical experiments on a tutorial example.
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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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Maddaloni, Alessandro, Ruben Matino, Ismael Matino, Stefano Dettori, Antonella Zaccara, and Valentina Colla. "A quadratic programming model for the optimization of off-gas networks in integrated steelworks." Matériaux & Techniques 107, no. 5 (2019): 502. http://dx.doi.org/10.1051/mattech/2019025.

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The European steel industry is constantly promoting developments, which can increase efficiency and lower the environmental impact of the steel production processes. In particular, a strong focus refers to the minimization of the energy consumption. This paper presents part of the work of the research project entitled “Optimization of the management of the process gas network within the integrated steelworks” (GASNET), which aims at developing a decision support system supporting energy managers and other concerned technical personnel in the implementation of an optimized off-gases management and exploitation considering environmental and economic objectives. A mathematical model of the network as a capacitated digraph with costs on arcs is proposed and an optimization problem is formulated. The objective of the optimization consists in minimizing the wastes of process gases and maximizing the incomes. Several production constraints need to be accounted. In particular, different types of gases are mixing in the same network. The constraints that model the mixing make the problem computationally difficult: it is a non-convex quadratically constrained quadratic program (QCQP). Two formulations of the problem are presented: the first one is a minimum cost flow problem, which is a linear program and is thus computationally fast to solve, but suitable only for a single gas network. The second formulation is a quadratically constrained quadratic program, which is slower, but covers more general cases, such as the ones, which are characterized by the interaction among multiple gas networks. A user-friendly graphical interface has been developed and tests over existing plant networks are performed and analyzed.
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Xu, Yangyang. "First-Order Methods for Constrained Convex Programming Based on Linearized Augmented Lagrangian Function." INFORMS Journal on Optimization 3, no. 1 (January 2021): 89–117. http://dx.doi.org/10.1287/ijoo.2019.0033.

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First-order methods (FOMs) have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two FOMs for constrained convex programs, where the constraint set is represented by affine equations and smooth nonlinear inequalities. Both methods are based on the classical augmented Lagrangian function. They update the multipliers in the same way as the augmented Lagrangian method (ALM) but use different primal updates. The first method, at each iteration, performs a single proximal gradient step to the primal variable, and the second method is a block update version of the first one. For the first method, we establish its global iterate convergence and global sublinear and local linear convergence, and for the second method, we show a global sublinear convergence result in expectation. Numerical experiments are carried out on the basis pursuit denoising, convex quadratically constrained quadratic programs, and the Neyman-Pearson classification problem to show the empirical performance of the proposed methods. Their numerical behaviors closely match the established theoretical results.
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Dissertations / Theses on the topic "Quadratically Constrained Linear Programming"

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P, Van Voorhis Timothy. "The quadratically constrained quadratic program." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/23379.

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Wang, Guanglei. "Relaxations in mixed-integer quadratically constrained programming and robust programming." Thesis, Evry, Institut national des télécommunications, 2016. http://www.theses.fr/2016TELE0026/document.

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De nombreux problèmes de la vie réelle sont exprimés sous la forme de décisions à prendre à l’aide de l’information accessible dans le but d’atteindre certains objectifs. La programmation numérique a prouvé être un outil efficace pour modéliser et résoudre une grande variété de problèmes de ce type. Cependant, de nombreux problèmes en apparence faciles sont encore durs à résoudre. Et même des problèmes faciles de programmation linéaire deviennent durs avec l’incertitude de l’information disponible. Motivés par un problème de télécommunication où l’on doit associer des machines virtuelles à des serveurs tout en minimisant les coûts, nous avons employé plusieurs outils de programmation mathématique dans le but de résoudre efficacement le problème, et développé de nouveaux outils pour des problèmes plus généraux. Dans l’ensemble, résumons les principaux résultats de cette thèse comme suit. Une formulation exacte et plusieurs reformulations pour le problème d’affectation de machines virtuelles dans le cloud sont données. Nous utilisons plusieurs inégalités valides pour renforcer la formulation exacte, accélérant ainsi l’algorithme de résolution de manière significative. Nous donnons en outre un résultat géométrique sur la qualité de la borne lagrangienne montrant qu’elle est généralement beaucoup plus forte que la borne de la relaxation continue. Une hiérarchie de relaxation est également proposée en considérant une séquence de couverture de l’ensemble de la demande. Ensuite, nous introduisons une nouvelle formulation induite par les symétries du problème. Cette formulation permet de réduire considérablement le nombre de termes bilinéaires dans le modèle, et comme prévu, semble plus efficace que les modèles précédents. Deux approches sont développées pour la construction d’enveloppes convexes et concaves pour l’optimisation bilinéaire sur un hypercube. Nous établissons plusieurs connexions théoriques entre différentes techniques et nous discutons d’autres extensions possibles. Nous montrons que deux variantes de formulations pour approcher l’enveloppe convexe des fonctions bilinéaires sont équivalentes. Nous introduisons un nouveau paradigme sur les problèmes linéaires généraux avec des paramètres incertains. Nous proposons une hiérarchie convergente de problèmes d’optimisation robuste – approche robuste multipolaire, qui généralise les notions de robustesse statique, de robustesse d’affinement ajustable, et de robustesse entièrement ajustable. En outre, nous montrons que l’approche multipolaire peut générer une séquence de bornes supérieures et une séquence de bornes inférieures en même temps et les deux séquences convergent vers la valeur robuste des FARC sous certaines hypothèses modérées
Many real life problems are characterized by making decisions with current information to achieve certain objectives. Mathematical programming has been developed as a successful tool to model and solve a wide range of such problems. However, many seemingly easy problems remain challenging. And some easy problems such as linear programs can be difficult in the face of uncertainty. Motivated by a telecommunication problem where assignment decisions have to be made such that the cloud virtual machines are assigned to servers in a minimum-cost way, we employ several mathematical programming tools to solve the problem efficiently and develop new tools for general theoretical problems. In brief, our work can be summarized as follows. We provide an exact formulation and several reformulations on the cloud virtual machine assignment problem. Then several valid inequalities are used to strengthen the exact formulation, thereby accelerating the solution procedure significantly. In addition, an effective Lagrangian decomposition is proposed. We show that, the bounds providedby the proposed Lagrangian decomposition is strong, both theoretically and numerically. Finally, a symmetry-induced model is proposed which may reduce a large number of bilinear terms in some special cases. Motivated by the virtual machine assignment problem, we also investigate a couple of general methods on the approximation of convex and concave envelopes for bilinear optimization over a hypercube. We establish several theoretical connections between different techniques and prove the equivalence of two seeming different relaxed formulations. An interesting research direction is also discussed. To address issues of uncertainty, a novel paradigm on general linear problems with uncertain parameters are proposed. This paradigm, termed as multipolar robust optimization, generalizes notions of static robustness, affinely adjustable robustness, fully adjustable robustness and fills the gaps in-between. As consequences of this new paradigms, several known results are implied. Further, we prove that the multipolar approach can generate a sequence of upper bounds and a sequence of lower bounds at the same time and both sequences converge to the robust value of fully adjustable robust counterpart under some mild assumptions
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Crowe, Mitch. "Nonlinearly constrained optimization via sequential regularized linear programming." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/29648.

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This thesis proposes a new active-set method for large-scale nonlinearly con strained optimization. The method solves a sequence of linear programs to generate search directions. The typical approach for globalization is based on damping the search directions with a trust-region constraint; our proposed ap proach is instead based on using a 2-norm regularization term in the objective. Numerical evidence is presented which demonstrates scaling inefficiencies in current sequential linear programming algorithms that use a trust-region constraint. Specifically, we show that the trust-region constraints in the trustregion subproblems significantly reduce the warm-start efficiency of these subproblem solves, and also unnecessarily induce infeasible subproblems. We also show that the use of a regularized linear programming (RLP) step largely elim inates these inefficiencies and, additionally, that the dual problem to RLP is a bound-constrained least-squares problem, which may allow for very efficient subproblem solves using gradient-projection-type algorithms. Two new algorithms were implemented and are presented in this thesis, based on solving sequences of RLPs and trust-region constrained LPs. These algorithms are used to demonstrate the effectiveness of each type of subproblem, which we extrapolate onto the effectiveness of an RLP-based algorithm with the addition of Newton-like steps. All of the source code needed to reproduce the figures and tables presented in this thesis is available online at http: //www.cs.ubc.ca/labs/scl/thesis/lOcrowe/
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Zhao, Jianmin. "Optimal Clustering: Genetic Constrained K-Means and Linear Programming Algorithms." VCU Scholars Compass, 2006. http://hdl.handle.net/10156/1583.

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Hardin, Jill Renea. "Resource-constrained scheduling and production planning : linear programming-based studies." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/24857.

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Wang, Yanhui. "Affine scaling algorithms for linear programs and linearly constrained convex and concave programs." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/24919.

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Viana, Luiz Alberto do Carmo. "Dependency constrained minimum spanning tree." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17302.

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FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico
Introduzimos o problema de Ãrvore Geradora com DependÃncias MÃnima, AGDM(G,D,w), definido sobre um grafo G(V,E) e um digrafo D(E,A), cujos vÃrtices sÃo as arestas de G e cujos arcos definem dependÃncias entre tais arestas. O problema consiste em encontrar, dentre as Ãrvores geradoras do grafo G(V,E) que satisfaÃam as restriÃÃes de dependÃncia impostas pelo digrafo de entrada D(E,A), uma que tenha custo mÃnimo, segundo a ponderaÃÃo w das arestas de G. As restriÃÃes de dependÃncia exigem que uma aresta e de G sà pode fazer parte de uma soluÃÃo se for uma fonte em D ou se fizer parte da soluÃÃo alguma outra aresta à tal que o arco (e′, e) esteja em D. Provamos que decidir se hà soluÃÃo viÃvel para AGDM(G,D,w) à um problema NP-completo, mesmo quando G à um cacto cordal e D à a uniÃo de arborescÃncias de altura no mÃximo 2. Sua NP-completude tambÃm à mostrada ainda que G seja bipartido, as restriÃÃes de dependÃncia ocorram apenas entre arestas adjacentes de G e formem arborescÃncias de altura no mÃximo 2. Resultados idÃnticos sÃo obtidos para as variantes do problema onde, nas restriÃÃes de dependÃncia, substitui-se o requisito âalgumaâ por âexatamente umaâ ou âtodaâ. Para resolver o problema, apresentamos algumas formulaÃÃes de programaÃÃo inteira e desigualdades vÃlidas. Propomos uma estratÃgia para reduzir a dimensÃo do problema, excluindo arestas de G com base na estrutura de D. Avaliamos os modelos e algoritmos propostos usando instÃncias geradas aleatoriamente. Resultados computacionais sÃo reportados.
We introduce the Dependency Constrained Minimum Spanning Tree Problem, DCMST(G,D,w), defined over a graph G(V,E) and a digraph D(E,A), whose vertices are the edges of G and whose arcs describe dependency relations between these edges. Such problem consists of finding, among the spanning trees of G(V,E) satisfying the dependency constraints imposed by D(E,A), that one whose cost is minimum, according to a edgeweight function w. The dependency constraints impose that an edge e of G can be part of a solution either if it is a source in D or if some other edge e′, such that the arc (e′, e) is in D, is part of it as well. We prove that deciding whether there is a feasible solution to DCMST(G,D,w) is an NP-complete problem, even if G is a chordal cactus and D is a union of arborescences of height at most 2. NP-completeness also applies if G is bipartite, the dependency constraints occur only between adjacent edges of G and their related arcs describe arborescences whose height is at most 2. The same results are obtained for the problem variants which demand that, instead of âsomeâ, âexactly oneâor âallâdependencies be part of a solution. To solve the problem, we introduce some integer programming formulations and some valid inequalities. We propose a strategy to reduce the problem dimension by excluding some edges of G according to the structure of D. We evaluate the introduced models and algorithms using randomly generated instances. Computational results are reported.
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Aslan, Murat. "The Cardinality Constrained Multiple Knapsack Problem." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12610131/index.pdf.

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The classical multiple knapsack problem selects a set of items and assigns each to one of the knapsacks so as to maximize the total profit. The knapsacks have limited capacities. The cardinality constrained multiple knapsack problem assumes limits on the number of items that are to be put in each knapsack, as well. Despite many efforts on the classical multiple knapsack problem, the research on the cardinality constrained multiple knapsack problem is scarce. In this study we consider the cardinality constrained multiple knapsack problem. We propose heuristic and optimization procedures that rely on the optimal solutions of the linear programming relaxation problem. Our computational results on the large-sized problem instances have shown the satisfactory performances of our algorithms.
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Pedroso, Lucas Garcia. "Programação não linear sem derivadas." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307473.

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Orientadores: Jose Mario Martinez, Maria Aparecida Diniz Ehrhardt
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-14T08:44:35Z (GMT). No. of bitstreams: 1 Pedroso_LucasGarcia_D.pdf: 1569234 bytes, checksum: 22491a86b6f7cc218acc26f3c2cb768a (MD5) Previous issue date: 2009
Resumo: Neste trabalho propomos um algoritmo Lagrangiano Aumentado sem derivadas para o problema geral de otimização. Consideramos o método introduzido por Andreani, Birgin, Martínez e Schuverdt, eliminando os cálculos de derivadas inerentes ao algoritmo através de modificações adequadas no critério de parada. Foram mantidos os bons resultados teóricos do método, como convergência sob a condição de qualificação CPLD e a limitação do parâmetro de penalidade. Experimentos numéricos são apresentados, entre os quais destacamos um exemplo de problema sem derivadas baseado na simulação de áreas de figuras no plano.
Abstract: We propose in this work a derivative-free Augmented Lagrangian algorithm for the general problem of optimization. We consider the method due to Andreani, Birgin, Martínez and Schuverdt, eliminating the derivative computations in the algorithm by making suitable modifications on the stopping criterion. The good theoretical results of the method were mantained, as convergence under the CPLD constraint qualification and the limitation of the penalty parameter. Numerical experiments are presented, and the most relevant of them is an example of derivative-free problem based on the simulation of areas of figures on the plane.
Doutorado
Otimização Matematica
Doutor em Matemática Aplicada
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Vanden, Berghen Frank. "Constrained, non-linear, derivative-free, parallel optimization of continuous, high computing load, noisy objective functions." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211177.

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The main result is a new original algorithm: CONDOR ("COnstrained, Non-linear, Direct, parallel Optimization using trust Region method for high-computing load, noisy functions"). The aim of this algorithm is to find the minimum x* of an objective function F(x) (x is a vector whose dimension is between 1 and 150) using the least number of function evaluations of F(x). It is assumed that the dominant computing cost of the optimization process is the time needed to evaluate the objective function F(x) (One evaluation can range from 2 minutes to 2 days). The algorithm will try to minimize the number of evaluations of F(x), at the cost of a huge amount of routine work. CONDOR is a derivate-free optimization tool (i.e. the derivatives of F(x) are not required. The only information needed about the objective function is a simple method (written in Fortran, C++,) or a program (a Unix, Windows, Solaris, executable) which can evaluate the objective function F(x) at a given point x. The algorithm has been specially developed to be very robust against noise inside the evaluation of the objective function F(x). This hypotheses are very general, the algorithm can thus be applied on a vast number of situations. CONDOR is able to use several CPU's in a cluster of computers. Different computer architectures can be mixed together and used simultaneously to deliver a huge computing power. The optimizer will make simultaneous evaluations of the objective function F(x) on the available CPU's to speed up the optimization process. The experimental results are very encouraging and validate the quality of the approach: CONDOR outperforms many commercial, high-end optimizer and it might be the fastest optimizer in its category (fastest in terms of number of function evaluations). When several CPU's are used, the performances of CONDOR are currently unmatched (may 2004). CONDOR has been used during the METHOD project to optimize the shape of the blades inside a Centrifugal Compressor (METHOD stands for Achievement Of Maximum Efficiency For Process Centrifugal Compressors THrough New Techniques Of Design). In this project, the objective function is based on a 3D-CFD (computation fluid dynamic) code which simulates the flow of the gas inside the compressor.
Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished
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Books on the topic "Quadratically Constrained Linear Programming"

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Xiaoqi, Yang, ed. Lagrange-type functions in constrained non-convex optimization. Boston: Kluwer Academic Publishers, 2003.

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Ryan, Michael J. A Model building approach to horticultural applications of linear programming and constrained games. Hull: University of Hull, Department of Economics, 1997.

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Yang, Xiao-qi, and Alexander M. Rubinov. Lagrange-type Functions in Constrained Non-Convex Optimization. Springer, 2013.

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Rubinov, A., and Xiao-qi Yang. Lagrange-type Functions in Constrained Non-Convex Optimization (Applied Optimization). Springer, 2003.

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Michel, Bierlaire. Optimization: Principles and Algorithms. EPFL Press, 2015. http://dx.doi.org/10.55430/6116v1mb.

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Every engineer and decision scientist must have a good mastery of optimization, an essential element in their toolkit. Thus, this articulate introductory textbook will certainly be welcomed by students and practicing professionals alike. Drawing from his vast teaching experience, the author skillfully leads the reader through a rich choice of topics in a coherent, fluid and tasteful blend of models and methods anchored on the underlying mathematical notions (only prerequisites: first year calculus and linear algebra). Topics range from the classics to some of the most recent developments in smooth unconstrained and constrained optimization, like descent methods, conjugate gradients, Newton and quasi-Newton methods, linear programming and the simplex method, trust region and interior point methods. Furthermore elements of discrete and combinatorial optimization like network optimization, integer programming and heuristic local search methods are also presented. This book presents optimization as a modeling tool that beyond supporting problem formulation plus design and implementation of efficient algorithms, also is a language suited for interdisciplinary human interaction. Readers further become aware that while the roots of mathematical optimization go back to the work of giants like Newton, Lagrange, Cauchy, Euler or Gauss, it did not become a discipline on its own until World War Two. Also that its present momentum really resulted from its symbiosis with modern computers, which made it possible to routinely solve problems with millions of variables and constraints. With his witty, entertaining, yet precise style, Michel Bierlaire captivates his readers and awakens their desire to try out the presented material in a creative mode. One of the outstanding assets of this book is the unified, clear and concise rendering of the various algorithms, which makes them easily readable and translatable into any high level programming language. ''This is an addictive book that I am very pleased to recommend.'' Prof. Thomas M. Liebling
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Book chapters on the topic "Quadratically Constrained Linear Programming"

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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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Shah, Nita H., and Poonam Prakash Mishra. "Constrained Multivariable Optimization." In Non-Linear Programming, 31–50. First edition. | Boca Raton, FL: CRC Press, an imprint of Taylor & Francis Group, LLC, 2021. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003105213-3.

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Shah, Nita H., and Poonam Prakash Mishra. "Constrained Multivariable Optimization." In Non-Linear Programming, 31–50. First edition. | Boca Raton, FL: CRC Press, an imprint of Taylor & Francis Group, LLC, 2021. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.4324/9781003105213-3.

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Luenberger, David G., and Yinyu Ye. "Constrained Minimization Conditions." In Linear and Nonlinear Programming, 321–57. New York, NY: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-74503-9_11.

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Luenberger, David G., and Yinyu Ye. "Constrained Minimization Conditions." In Linear and Nonlinear Programming, 321–55. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-18842-3_11.

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Jiang, Rujun, and Duan Li. "Semidefinite Programming Based Convex Relaxation for Nonconvex Quadratically Constrained Quadratic Programming." In Advances in Intelligent Systems and Computing, 213–20. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21803-4_22.

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Ku, Wen-Yang, and J. Christopher Beck. "Constraint Programming for Strictly Convex Integer Quadratically-Constrained Problems." In Lecture Notes in Computer Science, 316–32. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44953-1_21.

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Altman, Eitan. "The total cost: Dynamic and Linear Programming." In Constrained Markov Decision Processes, 117–35. Boca Raton: Routledge, 2021. http://dx.doi.org/10.1201/9781315140223-11.

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Mészáros, Csaba. "The Bpmpd Interior Point Solver for Convex Quadratically Constrained Quadratic Programming Problems." In Large-Scale Scientific Computing, 813–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12535-5_97.

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Mueller, Marianne, and Stefan Kramer. "Integer Linear Programming Models for Constrained Clustering." In Discovery Science, 159–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16184-1_12.

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Conference papers on the topic "Quadratically Constrained Linear Programming"

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Olkin, Julia A., and Paul J. Titterton, Jr. "Semidefinite programming for quadratically constrained quadratic programs." In SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Franklin T. Luk. SPIE, 1995. http://dx.doi.org/10.1117/12.211397.

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Amato, Christopher, Daniel S. Bernstein, and Shlomo Zilberstein. "Solving POMDPs using quadratically constrained linear programs." In the fifth international joint conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1160633.1160694.

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Khabbazibasmenj, Arash, and Sergiy A. Vorobyov. "Generalized quadratically constrained quadratic programming for signal processing." In ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014. http://dx.doi.org/10.1109/icassp.2014.6855084.

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Sun, Chuangchuang, and Ran Dai. "Spacecraft Attitude Control under Constrained Zones via Quadratically Constrained Quadratic Programming." In AIAA Guidance, Navigation, and Control Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-2010.

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Frison, Gianluca, Jonathan Frey, Florian Messerer, Andrea Zanelli, and Moritz Diehl. "Introducing the quadratically-constrained quadratic programming framework in HPIPM." In 2022 European Control Conference (ECC). IEEE, 2022. http://dx.doi.org/10.23919/ecc55457.2022.9838499.

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Cheng, Yongfang, Yin Wang, Mario Sznaier, and Octavia Camps. "Subspace Clustering with Priors via Sparse Quadratically Constrained Quadratic Programming." In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2016. http://dx.doi.org/10.1109/cvpr.2016.562.

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Sun, Chuangchuang, Ran Dai, and Ping Lu. "Multi-Phase Spacecraft Mission Optimization by Quadratically Constrained Quadratic Programming." In AIAA Scitech 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-1667.

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You, Sixiong, and Ran Dai. "Local Optimization of Nonconvex Mixed-Integer Quadratically Constrained Quadratic Programming Problems." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304368.

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Fakhry, R., Yasmine Abouelseoud, and Emtethal Negm. "Mixed-integer quadratically constrained programming with application to distribution networks reconfiguration." In 2016 Eighteenth International Middle East Power Systems Conference (MEPCON). IEEE, 2016. http://dx.doi.org/10.1109/mepcon.2016.7836950.

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Ye, Jieping, Shuiwang Ji, and Jianhui Chen. "Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming." In the 13th ACM SIGKDD international conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1281192.1281283.

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Reports on the topic "Quadratically Constrained Linear Programming"

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Ye, Y., O. Gueler, R. A. Tapia, and Y. Zhang. A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, August 1991. http://dx.doi.org/10.21236/ada455490.

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VAN BLOEMEN WAANDERS, BART G., ROSCOE A. BARTLETT, KEVIN R. LONG, PAUL T. BOGGS, and ANDREW G. SALINGER. Large Scale Non-Linear Programming for PDE Constrained Optimization. Office of Scientific and Technical Information (OSTI), October 2002. http://dx.doi.org/10.2172/805833.

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You might also be interested in the extended bibliographies on the topic 'Quadratically Constrained Linear Programming' for particular source types:
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