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Journal articles on the topic 'Quadratically Constrained Linear Programming'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Li, Minghuang, and Fusheng Yu. "Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data." International Journal of Fuzzy System Applications 1, no. 3 (July 2011): 32–46. http://dx.doi.org/10.4018/ijfsa.2011070103.

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Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

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12

Zhao, Yu, Xihong Chen, Lunsheng Xue, and Qun Zhang. "Design of Robust Pulses to Insufficient Synchronization for OFDM/OQAM Systems in Doubly Dispersive Channels." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/826192.

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This paper presents a pulse shaping method robust to insufficient synchronization in orthogonal frequency division multiplexing with offset quadrature amplitude modulation (OFDM/OQAM) systems over doubly dispersive (DD) channels. The proposed pulse is designed as a linear combination of several well localized Hermite functions. The coefficients optimization problem is modeled as a nonconvex constrained fractional programming problem based on the signal-to-interference ratio (SIR) maximization criterion. An efficient iterative algorithm is applied to simplify the problem to a series of quadratically constrained quadratic program (QCQP) problems which can be solved by semidefinite relaxation (SDR) method. Simulation results show that the proposed pulse is superior to traditional pulses with respect to SIR performance over DD channels in the presence of carrier frequency offset (CFO) and timing offset (TO).

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13

Adibi, Ali, and Ehsan Salari. "Scalable Optimization Methods for Incorporating Spatiotemporal Fractionation into Intensity-Modulated Radiotherapy Planning." INFORMS Journal on Computing 34, no. 2 (March 2022): 1240–56. http://dx.doi.org/10.1287/ijoc.2021.1070.

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It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

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14

Serna-Suárez, Iván David. "A Convex Approximation for Optimal DER Scheduling on Unbal-anced Power Distribution Networks." DYNA 86, no. 208 (January 1, 2019): 281–91. http://dx.doi.org/10.15446/dyna.v86n208.72886.

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The increase of solar photovoltaic penetration poses several challenges for distribution network operation, mainly because such high penetration might cause reliability problems like protection malfunctioning, accelerated decay of voltage regulators and voltage violations. Some control strategies avoid such drawbacks at the cost of not fully exploiting the available energy. Existing solutions based on mathematical programming solve a 3-phase ACOPF to optimally exploit the available energy, however, this might increase all reliability problems above if done carelessly. As a solution to optimally exploit DERs (like local photovoltaic and storage systems) without compromising the network reliability, this paper presents a novel algorithm to solve the 3-phase ACOPF as a sequence of convex Quadratically Constrained Quadratic Programs. Results show that this solution has a lower voltage unbalance and computation time than its non-linear counterpart, furthermore, it converges to a primal feasible point for the non-linear formulation without major sacrifices on optimal DER active power injections.

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15

Si, Weijian, Xinggen Qu, Yilin Jiang, and Tao Chen. "Multiple Sparse Measurement Gradient Reconstruction Algorithm for DOA Estimation in Compressed Sensing." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/152570.

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A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is proposed, in which the DOA estimation problem is cast as the joint sparse reconstruction from multiple measurement vectors (MMV). The proposed method is derived through transforming quadratically constrained linear programming (QCLP) into unconstrained convex optimization which overcomes the drawback thatl1-norm is nondifferentiable when sparse sources are reconstructed by minimizingl1-norm. The convergence rate and estimation performance of the proposed method can be significantly improved, since the steepest descent step and Barzilai-Borwein step are alternately used as the search step in the unconstrained convex optimization. The proposed method can obtain satisfactory performance especially in these scenarios with low signal to noise ratio (SNR), small number of snapshots, or coherent sources. Simulation results show the superior performance of the proposed method as compared with existing methods.

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16

Ouellet, Yanick, and Claude-Guy Quimper. "The SoftCumulative Constraint with Quadratic Penalty." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (June 28, 2022): 3813–20. http://dx.doi.org/10.1609/aaai.v36i4.20296.

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The Cumulative constraint greatly contributes to the success of constraint programming at solving scheduling problems. The SoftCumulative, a version of the Cumulative where overloading the resource incurs a penalty is, however, less studied. We introduce a checker and a filtering algorithm for the SoftCumulative, which are inspired by the powerful energetic reasoning rule for the Cumulative. Both algorithms can be used with classic linear penalty function, but also with a quadratic penalty function, where the penalty of overloading the resource increases quadratically with the amount of the overload. We show that these algorithms are more general than existing algorithms and vastly outperform a decomposition of the SoftCumulative in practice.

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17

Kim, Y., and M. Mesbahi. "Quadratically Constrained Attitude Control via Semidefinite Programming." IEEE Transactions on Automatic Control 49, no. 5 (May 2004): 731–35. http://dx.doi.org/10.1109/tac.2004.825959.

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18

XIA, YONG. "CONVEX HULL PRESENTATION OF A QUADRATICALLY CONSTRAINED SET AND ITS APPLICATION IN SOLVING QUADRATIC PROGRAMMING PROBLEMS." Asia-Pacific Journal of Operational Research 26, no. 06 (December 2009): 769–78. http://dx.doi.org/10.1142/s0217595909002468.

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In this article, we study the convex hull presentation of a quadratically constrained set. Applying the new result, we solve a kind of quadratically constrained quadratic programming problems, which generalizes many well-studied problems.

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19

Huang, Kejun, and Nicholas D. Sidiropoulos. "Consensus-ADMM for General Quadratically Constrained Quadratic Programming." IEEE Transactions on Signal Processing 64, no. 20 (October 15, 2016): 5297–310. http://dx.doi.org/10.1109/tsp.2016.2593681.

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20

Madani, Ramtin, Mohsen Kheirandishfard, Javad Lavaei, and Alper Atamtürk. "Penalized semidefinite programming for quadratically-constrained quadratic optimization." Journal of Global Optimization 78, no. 3 (June 21, 2020): 423–51. http://dx.doi.org/10.1007/s10898-020-00918-8.

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21

Anstreicher, Kurt M. "On convex relaxations for quadratically constrained quadratic programming." Mathematical Programming 136, no. 2 (October 27, 2012): 233–51. http://dx.doi.org/10.1007/s10107-012-0602-3.

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22

Solodov, M. V. "On the Sequential Quadratically Constrained Quadratic Programming Methods." Mathematics of Operations Research 29, no. 1 (February 2004): 64–79. http://dx.doi.org/10.1287/moor.1030.0069.

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23

Verriest, E. I., and G. A. Pajunen. "Quadratically saturated regulator for constrained linear systems." IEEE Transactions on Automatic Control 41, no. 7 (July 1996): 992–95. http://dx.doi.org/10.1109/9.508902.

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24

Hou, Zhisong, Hongwei Jiao, Lei Cai, and Chunyang Bai. "Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs." Open Mathematics 15, no. 1 (October 3, 2017): 1212–24. http://dx.doi.org/10.1515/math-2017-0099.

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Abstract This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

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25

Pawlak, Tomasz P., and Bartosz Litwiniuk. "Ellipsoidal one-class constraint acquisition for quadratically constrained programming." European Journal of Operational Research 293, no. 1 (August 2021): 36–49. http://dx.doi.org/10.1016/j.ejor.2020.12.018.

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26

Wu, Duzhi, Aiping Hu, Jie Zhou, and Songlin Wu. "A new convex relaxation for quadratically constrained quadratic programming." Filomat 27, no. 8 (2013): 1511–21. http://dx.doi.org/10.2298/fil1308511w.

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27

Melman, A. "A new linesearch method for quadratically constrained convex programming." Operations Research Letters 16, no. 2 (September 1994): 67–77. http://dx.doi.org/10.1016/0167-6377(94)90062-0.

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28

Ben-Tal, Aharon, and Marc Teboulle. "Hidden convexity in some nonconvex quadratically constrained quadratic programming." Mathematical Programming 72, no. 1 (January 1996): 51–63. http://dx.doi.org/10.1007/bf02592331.

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29

Herzel, Stefano, Maria Cristina Recchioni, and Francesco Zirilli. "A quadratically convergent method for linear programming." Linear Algebra and its Applications 152 (July 1991): 255–89. http://dx.doi.org/10.1016/0024-3795(91)90278-5.

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30

Jiang, Rujun, and Duan Li. "Second order cone constrained convex relaxations for nonconvex quadratically constrained quadratic programming." Journal of Global Optimization 75, no. 2 (June 5, 2019): 461–94. http://dx.doi.org/10.1007/s10898-019-00793-y.

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31

Zheng, Xiaojin, and Zhongyi Jiang. "Tighter quadratically constrained convex reformulations for semi-continuous quadratic programming." Journal of Industrial & Management Optimization 13, no. 5 (2017): 0. http://dx.doi.org/10.3934/jimo.2020071.

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32

Jian, Jin-bao, Qing-jie Hu, Chun-ming Tang, and Hai-yan Zheng. "A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions." Applied Mathematics and Optimization 56, no. 3 (August 31, 2007): 343–63. http://dx.doi.org/10.1007/s00245-007-9010-0.

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33

Anitescu, Mihai. "A Superlinearly Convergent Sequential Quadratically Constrained Quadratic Programming Algorithm for Degenerate Nonlinear Programming." SIAM Journal on Optimization 12, no. 4 (January 2002): 949–78. http://dx.doi.org/10.1137/s1052623499365309.

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34

Anstreicher, Kurt M. "Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming." Journal of Global Optimization 43, no. 2-3 (November 7, 2008): 471–84. http://dx.doi.org/10.1007/s10898-008-9372-0.

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Jiang, Shan, Shu-Cherng Fang, Tiantian Nie, and Qi An. "Structured linear reformulation of binary quadratically constrained quadratic programs." Optimization Letters 14, no. 3 (November 17, 2018): 611–36. http://dx.doi.org/10.1007/s11590-018-1361-8.

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36

Leon, Luis M., Arturo S. Bretas, and Sergio Rivera. "Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation." Energies 13, no. 13 (June 28, 2020): 3310. http://dx.doi.org/10.3390/en13133310.

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Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective.

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37

He, Xin, and Yik-Chung Wu. "Corrections to “Set Squeezing Procedure for Quadratically Perturbed Chance-Constrained Programming”." IEEE Transactions on Signal Processing 69 (2021): 1664. http://dx.doi.org/10.1109/tsp.2021.3061755.

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38

Arima, Naohiko, Sunyoung Kim, and Masakazu Kojima. "A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming." SIAM Journal on Optimization 23, no. 4 (January 2013): 2320–40. http://dx.doi.org/10.1137/120890636.

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39

Bao, Xiaowei, Nikolaos V. Sahinidis, and Mohit Tawarmalani. "Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons." Mathematical Programming 129, no. 1 (May 18, 2011): 129–57. http://dx.doi.org/10.1007/s10107-011-0462-2.

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40

Audet, Charles, Pierre Hansen, Brigitte Jaumard, and Gilles Savard. "A branch and cut algorithm for nonconvex quadratically constrained quadratic programming." Mathematical Programming 87, no. 1 (January 2000): 131–52. http://dx.doi.org/10.1007/s101079900106.

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41

Jian, Jin-bao, and Mian-tao Chao. "A sequential quadratically constrained quadratic programming method for unconstrained minimax problems." Journal of Mathematical Analysis and Applications 362, no. 1 (February 2010): 34–45. http://dx.doi.org/10.1016/j.jmaa.2009.08.046.

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42

Goldfarb, Donald, Shucheng Liu, and Siyun Wang. "A Logarithmic Barrier Function Algorithm for Quadratically Constrained Convex Quadratic Programming." SIAM Journal on Optimization 1, no. 2 (May 1991): 252–67. http://dx.doi.org/10.1137/0801017.

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43

Fukushima, Masao, Zhi-Quan Luo, and Paul Tseng. "A Sequential Quadratically Constrained Quadratic Programming Method for Differentiable Convex Minimization." SIAM Journal on Optimization 13, no. 4 (January 2003): 1098–119. http://dx.doi.org/10.1137/s1052623401398120.

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44

Lu, Cheng, Zhibin Deng, Jing Zhou, and Xiaoling Guo. "A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming." Journal of Global Optimization 73, no. 2 (December 12, 2018): 371–88. http://dx.doi.org/10.1007/s10898-018-0726-y.

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45

Luo, Hezhi, Xiaodi Bai, and Jiming Peng. "Enhancing Semidefinite Relaxation for Quadratically Constrained Quadratic Programming via Penalty Methods." Journal of Optimization Theory and Applications 180, no. 3 (October 20, 2018): 964–92. http://dx.doi.org/10.1007/s10957-018-1416-0.

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Goyal, Vandana, Namrata Rani, and Deepak Gupta. "Iterative Parametric Approach for Quadratically Constrained Bi-Level Multiobjective Quadratic Fractional Programming." Journal of Computational and Theoretical Nanoscience 17, no. 11 (November 1, 2020): 5046–51. http://dx.doi.org/10.1166/jctn.2020.9339.

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Abstract:

The paper proposed an iterative parametric approach procedure for solving Bi-level Multiobjective Quadratic Fractional Programming model. The Model is divided into two levels-upper and lower. In the first stage of the approach, a set of pareto optimal solutions of upper Level is obtained by converting the problem into equivalent single non-fractional parametric objective optimization problem by using parametric vector and ε-constraint method. Then for the second stage, the solution of upper level is followed by the lower level decision maker while finding solution with the proposed algorithm to obtain the best preferred solution. A numerical example is solved in the last to validate the feasibility of the approach.

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Goyal, Vandana, Namrata Rani, and Deepak Gupta. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming." OPSEARCH 58, no. 3 (January 10, 2021): 557–74. http://dx.doi.org/10.1007/s12597-020-00497-y.

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Jiang, Rujun, and Duan Li. "Simultaneous Diagonalization of Matrices and Its Applications in Quadratically Constrained Quadratic Programming." SIAM Journal on Optimization 26, no. 3 (January 2016): 1649–68. http://dx.doi.org/10.1137/15m1023920.

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Lu, Cheng, Shu-Cherng Fang, Qingwei Jin, Zhenbo Wang, and Wenxun Xing. "KKT Solution and Conic Relaxation for Solving Quadratically Constrained Quadratic Programming Problems." SIAM Journal on Optimization 21, no. 4 (October 2011): 1475–90. http://dx.doi.org/10.1137/100793955.

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Keyanpour, Mohammad, and Naser Osmanpour. "On solving quadratically constrained quadratic programming problem with one non-convex constraint." OPSEARCH 55, no. 2 (March 3, 2018): 320–36. http://dx.doi.org/10.1007/s12597-018-0334-0.

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