Journal articles on the topic 'Quadratic matrix programs'
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JEYAKUMAR, VAITHILINGAM, and ZHIYOU WU. "CONDITIONS FOR GLOBAL OPTIMALITY OF QUADRATIC MINIMIZATION PROBLEMS WITH LMI CONSTRAINTS." Asia-Pacific Journal of Operational Research 24, no. 02 (April 2007): 149–60. http://dx.doi.org/10.1142/s021759590700119x.
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In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints.
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Han, Congying, Mingqiang Li, Tong Zhao, and Tiande Guo. "An Accelerated Proximal Gradient Algorithm for Singly Linearly Constrained Quadratic Programs with Box Constraints." Scientific World Journal 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/246596.
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Recently, the existed proximal gradient algorithms had been used to solve non-smooth convex optimization problems. As a special nonsmooth convex problem, the singly linearly constrained quadratic programs with box constraints appear in a wide range of applications. Hence, we propose an accelerated proximal gradient algorithm for singly linearly constrained quadratic programs with box constraints. At each iteration, the subproblem whose Hessian matrix is diagonal and positive definite is an easy model which can be solved efficiently via searching a root of a piecewise linear function. It is proved that the new algorithm can terminate at anε-optimal solution withinO(1/ε)iterations. Moreover, no line search is needed in this algorithm, and the global convergence can be proved under mild conditions. Numerical results are reported for solving quadratic programs arising from the training of support vector machines, which show that the new algorithm is efficient.
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Ahyaningsih, Faiz. "The Other Assignment For Problem Instances Esc 16b, Esc 16c And Esc 16h." Talenta Conference Series: Science and Technology (ST) 1, no. 1 (October 17, 2018): 044–48. http://dx.doi.org/10.32734/st.v1i1.188.
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The quadratic assigment problem (QAP) has remainedone of the great challenges in combinatorial optimization. In this paper I propose two programs, the MATLAB program for solving QAP, and the MATLAB program for checking objective value, if we input an arbitrary permutation, matrix flow and matrix distance. The first program using combination methods that combines random point strategy, forward exchange strategy , and backward exchange strategy. I‘ve tried my program to solve Esc 16b, Esc 16c and Esc 16h from QAPLIB (A Quadratic Assignment Problem Library). In the 500th iteration optimal value reached and I‘ve found the other assignment for problem instances Esc 16b, Esc 16c, and Esc 16h.
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Psilovikos, Aris, and Christos Tzimopoulos. "Comparison of quadratic and non-linear programming (QP and NLP) optimization models in groundwater management." Journal of Hydroinformatics 6, no. 3 (July 1, 2004): 175–85. http://dx.doi.org/10.2166/hydro.2004.0014.
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This project is concerned with the comparison of two algorithms used in groundwater management models, based on Quadratic Programming (QP) and Non-linear Programming (NLP) models. A quadratic objective function is used and solved in two different ways. The first one is the application of the Karush–Kuhn–Tücker (KKT) conditions and Wolfe's algorithm, which are used in solving QP models. The second one is the Conjugate Gradient Method (CGM), which is used in solving NLP models. Two additional ‘shell programs’ are created to formulate the results of the management model. These results are organized in a Mathematical Programming System (MPS) file. This is the management model output and contains the response matrix coefficients and all the management model details in a coded format. The MPS data file is formatted via the two shell programs, constituting the import data file for the optimization procedure that takes place with the GINO model and spreadsheets. An application took place in an aquifer in Northern Greece, just on the border with the Former Yugoslavian Republic of Macedonia (FYROM). The phreatic aquifer was divided into 271 small square areas, 200 m wide. The total area of the aquifer was 10.84 km2. The time increment was equal to 1 month. Finally, the comparison of the two different optimization algorithms took place, concerning the pumping rates, the managed head distribution and the optimum pumping cost.
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Garstka, Michael, Mark Cannon, and Paul Goulart. "COSMO: A Conic Operator Splitting Method for Convex Conic Problems." Journal of Optimization Theory and Applications 190, no. 3 (August 29, 2021): 779–810. http://dx.doi.org/10.1007/s10957-021-01896-x.
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AbstractThis paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package for convex optimisation problems with quadratic objective function and conic constraints. At each step, the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark problems show the effectiveness of our approach. Our Julia implementation is open source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.
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Li, Xin Min, Bao Ming Bai, and Juan Zhao. "SDR-Based Precoding for Multi-User Multi-Stream MIMO Downlinks." Applied Mechanics and Materials 543-547 (March 2014): 2004–8. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2004.
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The existing methods based on convex-optimization theory, which use the concept of SINR, can just design the optimal precoder for each user with single antenna. In this paper, we design the optimal precoding matrices for multi-user MIMO downlinks by solving the optimization problem that minimizes total transmit power subject to signal-leakage-plus-noise-ratio (SLNR) constraints. Because SLNR of each user is determined by its own precoding matrix and is independent of other users, the goal problem can be separated into a series of decoupled low-complexity quadratically constrained quadratic programs (QCQPs). Using the semidefinite relaxation (SDR) technique, these QCQPs can be reformulated into the semidefinite programs (SDP) and be solved effectively. Simulation results show that proposed precoding scheme is quite feasible when each user has two receive antennas, and it has better bit error rate (BER) performance than the original maximal-SLNR precoding scheme when SLNR of each user satisfies large threshold value.
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Keller, André A. "Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (August 1, 2015): 129–43. http://dx.doi.org/10.1515/jmbm-2015-0015.
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AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are replaced by new numerous pairwise products of the constraints. In the linearization phase, each distinct quadratic term is replaced by a single new RLT variable. This RLT process produces an LP relaxation. The LP-RLT yieds a lower bound on the global minimum. LMI formulations (linear matrix inequalities) have been proposed to treat efficiently with nonconvex sets. An LMI is equivalent to a system of polynomial inequalities. A semialgebraic convex set describes the system. The feasible sets are spectrahedra with curved faces, contrary to the LP case with polyhedra. Successive LMI relaxations of increasing size yield the global optimum. Nonlinear inequalities are converted to an LMI form using Schur complements. Optimizing a nonconvex polynomial is equivalent to the LP over a convex set. Engineering application interests include system analysis, control theory, combinatorial optimization, statistics, and structural design optimization.
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Zuo, Xuewu, Bilal Ahmad Rather, Muhammad Imran, and Akbar Ali. "On Some Topological Indices Defined via the Modified Sombor Matrix." Molecules 27, no. 19 (October 10, 2022): 6772. http://dx.doi.org/10.3390/molecules27196772.
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Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)−1/2 over all of the edges vivj of G. The modified Sombor matrix AMS(G) of G is the n by n matrix such that its (i,j)-entry is equal to (dvi2+dvj2)−1/2 when vi and vj are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of AMS(G). The sum of the absolute eigenvalues of AMS(G) is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is 2; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.
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Badenbroek, Riley, and Etienne de Klerk. "An Analytic Center Cutting Plane Method to Determine Complete Positivity of a Matrix." INFORMS Journal on Computing 34, no. 2 (March 2022): 1115–25. http://dx.doi.org/10.1287/ijoc.2021.1108.
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We propose an analytic center cutting plane method to determine whether a matrix is completely positive and return a cut that separates it from the completely positive cone if not. This was stated as an open (computational) problem by Berman et al. [Berman A, Dur M, Shaked-Monderer N (2015) Open problems in the theory of completely positive and copositive matrices. Electronic J. Linear Algebra 29(1):46–58]. Our method optimizes over the intersection of a ball and the copositive cone, where membership is determined by solving a mixed-integer linear program suggested by Xia et al. [Xia W, Vera JC, Zuluaga LF (2020) Globally solving nonconvex quadratic programs via linear integer programming techniques. INFORMS J. Comput. 32(1):40–56]. Thus, our algorithm can, more generally, be used to solve any copositive optimization problem, provided one knows the radius of a ball containing an optimal solution. Numerical experiments show that the number of oracle calls (matrix copositivity checks) for our implementation scales well with the matrix size, growing roughly like [Formula: see text] for d × d matrices. The method is implemented in Julia and available at https://github.com/rileybadenbroek/CopositiveAnalyticCenter.jl . Summary of Contribution: Completely positive matrices play an important role in operations research. They allow many NP-hard problems to be formulated as optimization problems over a proper cone, which enables them to benefit from the duality theory of convex programming. We propose an analytic center cutting plane method to determine whether a matrix is completely positive by solving an optimization problem over the copositive cone. In fact, we can use our method to solve any copositive optimization problem, provided we know the radius of a ball containing an optimal solution. We emphasize numerical performance and stability in developing this method. A software implementation in Julia is provided.
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Zhou, Jing. "A New Spatial Branch and Bound Algorithm for Quadratic Program with One Quadratic Constraint and Linear Constraints." Mathematical Problems in Engineering 2020 (February 25, 2020): 1–8. http://dx.doi.org/10.1155/2020/5717301.
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This paper proposes a novel second-order cone programming (SOCP) relaxation for a quadratic program with one quadratic constraint and several linear constraints (QCQP) that arises in various real-life fields. This new SOCP relaxation fully exploits the simultaneous matrix diagonalization technique which has become an attractive tool in the area of quadratic programming in the literature. We first demonstrate that the new SOCP relaxation is as tight as the semidefinite programming (SDP) relaxation for the QCQP when the objective matrix and constraint matrix are simultaneously diagonalizable. We further derive a spatial branch-and-bound algorithm based on the new SOCP relaxation in order to obtain the global optimal solution. Extensive numerical experiments are conducted between the new SOCP relaxation-based branch-and-bound algorithm and the SDP relaxation-based branch-and-bound algorithm. The computational results illustrate that the new SOCP relaxation achieves a good balance between the bound quality and computational efficiency and thus leads to a high-efficiency global algorithm.
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Astahin, A. S., and L. A. Tretyakova. "Management of life modelling of regional socio-economic systems." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 4 (February 11, 2020): 218–25. http://dx.doi.org/10.20914/2310-1202-2019-4-218-225.
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The study posed and solved the problems of theoretical and methodological substantiation of the management of modeling of the provision of vital functions of the population and the functioning of national economic facilities. An approach to modeling the level of life and stability of the region’s dynamic systems is presented. The mathematical apparatus and methodological support were used using the methods of linear matrix inequalities and non-quadratic Lyapunov vector functions, together with the method of optimizing linear series of a combination of partial and average values of integrated socio-economic indicators. Methods for evaluating managerial decisions and differentiating regions at the level of constituent entities of the Russian Federation are proposed and tested using the example of Vladimir, Ivanovo and Ryazan regions. Studies have established that the level of economic viability of the population is a priority indicator in characterizing the level and quality of public administration and determining the differentiation of a region (territory). As a result of the analysis, we came to the conclusion that the solution to the problems of increasing the sustainability of the economic development of regional economies should be associated with the following processes: strategic management as a continuous process of substantiating and selecting promising goals for the sustainable development of the region and developing specific plans and programs to achieve these goals; financial modeling as a system of forms, methods and techniques for managing cash flows, financial and material resources of the region, aimed at ensuring sustainable development of the territory; optimization of production and technical activities as a set of methods, principles and management tools for the transition to modern technologies and environmental quality standards; legal regulation as a process of targeted impact on social, economic, environmental and social relations occurring in the region, with the help of legal (legal) institutions; formation of the organizational structure and strengthening of the administrative resource (intensification of the impact of socio-political forces on socio-economic development). In these conditions, one of the guarantors of the implementation of measures to achieve balance and sustainable development should be local authorities.
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JI, SHUHUI, XIAOJIN ZHENG, and XIAOLING SUN. "AN IMPROVED CONVEX 0-1 QUADRATIC PROGRAM REFORMULATION FOR CHANCE-CONSTRAINED QUADRATIC KNAPSACK PROBLEMS." Asia-Pacific Journal of Operational Research 30, no. 03 (June 2013): 1340009. http://dx.doi.org/10.1142/s0217595913400095.
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We consider a chance-constrained quadratic knapsack problem (CQKP) where each item has a random size that is finitely distributed. We present a new convex 0-1 quadratic program reformulation for CQKP. This new reformulation improves the existing reformulation for general 0-1 quadratic program based on diagonal perturbation in the sense that the continuous relaxation of the new reformulation is tighter than or at least as tight as that of the existing reformulation. The improved reformulation is derived from a general matrix decomposition of the objective function and piecewise linearization of 0-1 variables. We show that the optimal parameters in the improved reformulation can be obtained by solving an SDP problem. Extension to k-item probabilistic quadratic knapsack problems is also discussed. Preliminary comparison results are reported to demonstrate the effectiveness of the improved reformulation.
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Shan, Xiao, and J. N. L. Connor. "Application of Heisenberg’s S Matrix Program to the Angular Scattering of the H + D2(vi = 0, ji = 0) → HD(vf = 3, jf = 0) + D Reaction: Piecewise S Matrix Elements Using Linear, Quadratic, Step-Function, and Top-Hat Parametrizations." Journal of Physical Chemistry A 116, no. 46 (August 28, 2012): 11414–26. http://dx.doi.org/10.1021/jp306435t.
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CONCENÇO, G., A. ANDRES, F. SCHREIBER, I. S. MOISINHO, M. C. CORADINI, and M. B. MARTINS. "WEED SPECIES ASSOCIATION IN ARABLE FIELDS: OLD APPROACH, NEW APPLICATION." Experimental Agriculture 55, no. 3 (January 25, 2018): 359–70. http://dx.doi.org/10.1017/s0014479718000029.
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SUMMARYWe aimed to assess the potential of the characterization of association among weed species as a tool to understand weed occurrence for further supporting long-term management programs. After a sequence of summer crops, which included irrigated rice and sorghum, the experimental area was submitted to subsoiling, limestone was applied, and ryegrass was planted in the winter season. Six months later, an ACCase-inhibitor herbicide was used to select only non-grassweed species. Field survey was carried out on 100 quadrats with 0.5-m width that were randomly sampled. Plant species were organized in 2 × 2 contingency tables. The results of the calculated chi-squares were compared to the respective tables, and results were presented as a paired chi-square matrix. The species–area curve was also obtained. The relative occurrence of species was determined by its frequency and presented as a wordcloud. The network analysis was obtained by using the Fruchterman–Reingold layout. The hypothesis of plant association aiming survival in arable fields was validated. The methodology of plant association based on the chi-square test was applicable to arable fields, where weed species (usually competitor plant types) occur in clusters. From a practical point of view, preference should be given to herbicides that are efficient on most species within a given cluster.
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Cen, Xiaoli, and Yong Xia. "A New Global Optimization Scheme for Quadratic Programs with Low-Rank Nonconvexity." INFORMS Journal on Computing, February 9, 2021. http://dx.doi.org/10.1287/ijoc.2020.1017.
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We consider the classical convex constrained nonconvex quadratic programming problem where the Hessian matrix of the objective to be minimized has r negative eigenvalues, denoted by (QPr). Based on a biconvex programming reformulation in a slightly higher dimension, we propose a novel branch-and-bound algorithm to solve (QP1) and show that it returns an [Formula: see text]-approximate solution of (QP1) in at most [Formula: see text] iterations. We further extend the new algorithm to solve the general (QPr) with r > 1. Computational comparison shows the efficiency of our proposed global optimization method for small r. Finally, we extend the explicit relaxation approach for (QP1) to (QPr) with r > 1. Summary of Contribution: Nonconvex quadratic program (QP) is a classical optimization problem in operations research. This paper aims at globally solving the QP where the Hessian matrix of the objective to be minimized has r negative eigenvalues. It is known to be nondeterministic polynomial-time hard even when r = 1. This paper presents a novel algorithm to globally solve the QP for r = 1 and then extends to general r. Numerical results demonstrate the superiority of the proposed algorithm in comparison with state-of-the-art algorithms/software for small r.
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Jiang, Rujun, and Duan Li. "Exactness Conditions for Semidefinite Programming Relaxations of Generalization of the Extended Trust Region Subproblem." Mathematics of Operations Research, August 23, 2022. http://dx.doi.org/10.1287/moor.2022.1305.
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The extended trust region subproblem (ETRS) of minimizing a quadratic objective over the unit ball with additional linear constraints has attracted a lot of attention in the last few years because of its theoretical significance and wide spectra of applications. Several sufficient conditions to guarantee the exactness of its semidefinite programming (SDP) relaxation have been recently developed in the literature. In this paper, we consider a generalization of the extended trust region subproblem (GETRS), in which the unit ball constraint in the ETRS is replaced by a general, possibly nonconvex, quadratic constraint, and the linear constraints are replaced by a conic linear constraint. We derive sufficient conditions for guaranteeing the exactness of the SDP relaxation of the GETRS under mild assumptions. Our main tools are two classes of convex relaxations for the GETRS based on either a simultaneous diagonalization transformation of the quadratic forms or linear combinations of the quadratic forms. We also compare our results to the existing sufficient conditions in the literature. Finally, we extend our results to derive a new sufficient condition for the exactness of the SDP relaxation of general diagonal quadratically constrained quadratic programs, where each quadratic function is associated with a diagonal matrix.
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Mai, Ngoc Hoang Anh, Jean-Bernard Lasserre, Victor Magron, and Jie Wang. "Exploiting constant trace property in large-scale polynomial optimization." ACM Transactions on Mathematical Software, August 8, 2022. http://dx.doi.org/10.1145/3555309.
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We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result, such moment relaxations can be solved efficiently by first-order methods that exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. We also extend this CTP-exploiting framework to large-scale POPs with different sparsity structures. The efficiency and scalability of our framework are illustrated on some moment relaxations for various randomly generated POPs, especially second-order moment relaxations for quadratically constrained quadratic programs.
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Aragón-Artacho, F. J., R. Campoy, and P. T. Vuong. "The Boosted DC Algorithm for Linearly Constrained DC Programming." Set-Valued and Variational Analysis, December 21, 2022. http://dx.doi.org/10.1007/s11228-022-00656-x.
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AbstractThe Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation step from the point computed by DCA via a line search procedure. In this work, we propose an extension of BDCA that can be applied to difference of convex functions programs with linear constraints, and prove that every cluster point of the sequence generated by this algorithm is a Karush–Kuhn–Tucker point of the problem if the feasible set has a Slater point. When the objective function is quadratic, we prove that any sequence generated by the algorithm is bounded and R-linearly (geometrically) convergent. Finally, we present some numerical experiments where we compare the performance of DCA and BDCA on some challenging problems: to test the copositivity of a given matrix, to solve one-norm and infinity-norm trust-region subproblems, and to solve piecewise quadratic problems with box constraints. Our numerical results demonstrate that this new extension of BDCA outperforms DCA.
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Argue, C. J., Fatma Kılınç-Karzan, and Alex L. Wang. "Necessary and Sufficient Conditions for Rank-One-Generated Cones." Mathematics of Operations Research, May 20, 2022. http://dx.doi.org/10.1287/moor.2022.1254.
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A closed convex conic subset [Formula: see text] of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of [Formula: see text] is closely related to the exactness of semidefinite program (SDP) relaxations of nonconvex quadratically constrained quadratic programs (QCQPs) related to [Formula: see text]. We consider the case where [Formula: see text] is obtained as the intersection of the PSD cone with finitely many homogeneous linear matrix inequalities and conic constraints and identify sufficient conditions that guarantee that [Formula: see text] is ROG. Our general framework allows us to recover a number of well-known results from the literature. In the case of two linear matrix inequalities, we also establish the necessity of our sufficient conditions. This extends one of the few settings from the literature—the case of one linear matrix inequality and the S-lemma—where an explicit characterization for the ROG property exists. Finally, we show how our ROG results on cones can be translated into inhomogeneous SDP exactness results and convex hull descriptions in the original space of a QCQP. We close with a few applications of these results; specifically, we recover the well-known perspective reformulation of a simple mixed-binary set via the ROG toolkit.
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Jansen, Klaus, Kim-Manuel Klein, and Alexandra Lassota. "The double exponential runtime is tight for 2-stage stochastic ILPs." Mathematical Programming, May 28, 2022. http://dx.doi.org/10.1007/s10107-022-01837-0.
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AbstractWe consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form $$\min \{c^T x \mid {\mathcal {A}} x = b, \ell \le x \le u, x \in {\mathbb {Z}}^{r + ns} \}$$ min { c T x ∣ A x = b , ℓ ≤ x ≤ u , x ∈ Z r + n s } where the constraint matrix $${\mathcal {A}} \in {\mathbb {Z}}^{nt \times r +ns}$$ A ∈ Z n t × r + n s consists of n matrices $$A_i \in {\mathbb {Z}}^{t \times r}$$ A i ∈ Z t × r on the vertical line and n matrices $$B_i \in {\mathbb {Z}}^{t \times s}$$ B i ∈ Z t × s on the diagonal line aside. We show a stronger hardness result for a number theoretic problem called Quadratic Congruences where the objective is to compute a number $$z \le \gamma $$ z ≤ γ satisfying $$z^2 \equiv \alpha \bmod \beta $$ z 2 ≡ α mod β for given $$\alpha , \beta , \gamma \in {\mathbb {Z}}$$ α , β , γ ∈ Z . This problem was proven to be NP-hard already in 1978 by Manders and Adleman. However, this hardness only applies for instances where the prime factorization of $$\beta $$ β admits large multiplicities of each prime number. We circumvent this necessity proving that the problem remains NP-hard, even if each prime number only occurs constantly often. Using this new hardness result for the $$\textsc {Quadratic Congruences}$$ Q U A D R A T I C C O N G R U E N C E S problem, we prove a lower bound of $$2^{2^{\delta (s+t)}} |I|^{O(1)}$$ 2 2 δ ( s + t ) | I | O ( 1 ) for some $$\delta > 0$$ δ > 0 for the running time of any algorithm solving 2-stage stochastic ILPs assuming the Exponential Time Hypothesis (ETH). Here, |I| is the encoding length of the instance. This result even holds if r, $$||b||_{\infty }$$ | | b | | ∞ , $$||c||_{\infty }, ||\ell ||_{\infty }$$ | | c | | ∞ , | | ℓ | | ∞ and the largest absolute value $$\varDelta $$ Δ in the constraint matrix $${\mathcal {A}}$$ A are constant. This shows that the state-of-the-art algorithms are nearly tight. Further, it proves the suspicion that these ILPs are indeed harder to solve than the closely related $$n$$ n -fold ILPs where the constraint matrix is the transpose of $${\mathcal {A}}$$ A .