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The neuro-dynamic scheme for solving general form of discrete time optimal control problems

APPLIED INTELLIGENCE 2018年第9期48卷 3178-3191页

作者： Nazemi, Alireza Sukhtsaraie, Samira Mortezaee, Marzieh Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran

In this paper, we show that recently developed neural network methods for quadratic programming can be put to use in solving discrete time optimal control problems, with general pointwise constraints on states and controls. We describe a high performance recurrent neural network for a discrete time linear quadratic regulator problem with mixed state-control constraints. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the discrete time problem. It is also shown that the proposed network model is stable in the Lyapunov sense and it is globally convergent to an exact optimal solution of the original problem. Several practical examples are provided to show the feasibility and the efficiency of the scheme.

关键词： Discrete time optimal control Neural network convex quadratic programming Convergent Stability

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Optimizing Bernoulli routing policies for balancing loads on call centers and minimizing transmission costs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期100卷 623-659页

作者： Servi, LD Humair, S MIT Ctr Operat Res Cambridge MA 02139 USA

We address the problem of assigning probabilities at discrete time instants for routing toll-free calls to a given set of call centers to minimize a weighted sum of transmission costs and load variability at the call centers during the next time interval. We model the problem as a tripartite graph and decompose the finding of an optimal probability assignment in the graph into the following problems: (i) estimating the true arrival rates at the nodes for the last time period;(ii) computing routing probabilities assuming that the estimates are correct. We use a simple approach for arrival rate estimation and solve the routing probability assignment by formulating it as a convex quadratic program and using the affine scaling algorithm to obtain an optimal solution. We further address a practical variant of the problem that involves changing routing probabilities associated with k nodes in the graph, where k is a prespecified number, to minimize the objective function. This involves deciding which k nodes to select for changing probabilities and determining the optimal value of the probabilities. We solve this problem using a heuristic that ranks all subsets of k nodes using gradient information around a given probability assignment. The routing model and the heuristic are evaluated for speed of computation of optimal probabilities and load balancing performance using a Monte Carlo simulation. Empirical results for load balancing are presented for a tripartite graph with 99 nodes and 17 call center gates.

关键词： call centers Bernoulli routing M/M/k queues rate estimation convex quadratic programming affine scaling method

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Asymptotic behavior of the central path for a special class of degenerate SDP problems

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MATHEMATICAL programming 2005年第3期103卷 487-514页

作者： Neto, JXD Ferreira, OP Monteiro, RDC Univ Fed Piaui BR-64049500 Teresina PI Brazil Univ Fed Goias BR-74001970 Goiania Go Brazil Georgia Inst Technol Sch ISyE Atlanta GA 30332 USA

This paper studies the asymptotic behavior of the central path (X(nu), S(nu), y(nu)) as nu down arrow 0 for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose "degenerate diagonal blocks" X-T(nu) and S-T(nu) of the central path are assumed to satisfy max{||X-T(nu)||, ||S-T(nu)||} = O(root nu). We establish the convergence of the central path towards a primal-dual optimal solution, which is characterized as being the unique optimal solution of a certain log-barrier problem. A characterization of the class of SDP problems which satisfy our assumptions are also provided. It is shown that the re-parametrization t > 0 -> (X(t(4)), S(t(4)), y(t(4))) of the central path is analytic at t = 0. The limiting behavior of the derivative of the central path is also investigated and it is shown that the order of convergence of the central path towards its limit point is O(root nu). Finally, we apply our results to the convex quadratically constrained convex programming (CQCCP) problem and characterize the class of CQCCP problems which can be formulated as SDPs satisfying the assumptions of this paper. In particular, we show that CQCCP problems with either a strictly convex objective function or at least one strictly convex constraint function lie in this class.

关键词： limiting behavior central path semidefinite programming convex quadratic programming convex quadratically constrained programming

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Superposition Signaling in Broadcast Interference Networks

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IEEE TRANSACTIONS ON COMMUNICATIONS 2017年第11期65卷 4646-4656页

作者： Hoang Duong Tuan Ho Huu Minh Tam Nguyen, Ha H. Duong, Trung Q. Poor, H. Vincent Univ Technol Sydney Sch Elect & Data Engn Ultimo NSW 2007 Australia Univ Technol Sydney Fac Engn & Informat Technol Ultimo NSW 2007 Australia Thinxtra Solution Pty Sydney NSW 2015 Australia Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK S7N 5A9 Canada Queens Univ Belfast Belfast BT7 1NN Antrim North Ireland Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

It is known that superposition signaling in Gaussian interference networks is capable of improving the achievable rate region. However, the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive, even in the simplest case of two-user single-input single-output interference networks. This paper examines superposition signaling for the general multiple-input multiple-output broadcast Gaussian interference networks. The problem of maximizing either the sum rate or the minimal user's rate under superposition signaling and dirty paper coding is solved by a computationally efficient path-following procedure, which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution. Numerical results demonstrate the substantial performance advantage of the proposed approach.

关键词： Gaussian interference networks multi-user MIMO superposition signaling convex quadratic programming

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An Improved TA-SVM Method Without Matrix Inversion and Its Fast Implementation for Nonstationary Datasets

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2015年第9期26卷 2005-2018页

作者： Shi, Yingzhong Chung, Fu-Lai Wang, Shitong Jiangnan Univ Sch Digital Media Wuxi 214122 Peoples R China Hong Kong Polytech Univ Dept Comp Hong Kong Hong Kong Peoples R China

Recently, a time-adaptive support vector machine (TA-SVM) is proposed for handling nonstationary datasets. While attractive performance has been reported and the new classifier is distinctive in simultaneously solving several SVM subclassifiers locally and globally by using an elegant SVM formulation in an alternative kernel space, the coupling of subclassifiers brings in the computation of matrix inversion, thus resulting to suffer from high computational burden in large nonstationary dataset applications. To overcome this shortcoming, an improved TA-SVM (ITA-SVM) is proposed using a common vector shared by all the SVM subclassifiers involved. ITA-SVM not only keeps an SVM formulation, but also avoids the computation of matrix inversion. Thus, we can realize its fast version, that is, improved time-adaptive core vector machine (ITA-CVM) for large nonstationary datasets by using the CVM technique. ITA-CVM has the merit of asymptotic linear time complexity for large nonstationary datasets as well as inherits the advantage of TA-SVM. The effectiveness of the proposed classifiers ITA-SVM and ITA-CVM is also experimentally confirmed.

关键词： convex quadratic programming core vector machine (CVM) drift concepts large nonstationary datasets time complexity

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A comparison of reduced and unreduced KKT systems arising from interior point methods

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第1期68卷 1-27页

作者： Morini, Benedetta Simoncini, Valeria Tani, Mattia Univ Bologna Dipartimento Matemat Piazza Porta S Donato 5 I-40127 Bologna Italy Univ Firenze Dipartimento Ingn Ind Viale GB Morgagni 40 I-50134 Florence Italy Univ Pavia Dipartimento Matemat Via A Ferrata 1 I-27100 Pavia Italy

We address the iterative solution of KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix is discussed. A theoretical and experimental analysis is conducted to assess which of the two formulations should be preferred for solving large-scale problems.

关键词： convex quadratic programming Interior point methods KKT systems Preconditioners

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Diversity-Based Random Forests with Sample Weight Learning

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COGNITIVE COMPUTATION 2019年第5期11卷 685-696页

作者： Yang, Chun Yin, Xu-Cheng Univ Sci & Technol Beijing Sch Comp & Commun Engn Dept Comp Sci & Technol Beijing 100083 Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing Key Lab Mat Sci Knowledge Engn Beijing 100083 Peoples R China Univ Sci & Technol Beijing Inst Artificial Intelligence Beijing 100083 Peoples R China

Given a variety of classifiers, one prevalent approach in classifier ensemble is to diversely combine classifier components, i.e., diversity-based ensembles, and a lot of previous works show that these ensembles can improve classification accuracy. Random forests are one of the most important ensembles. However, most random forests approaches with diversity-related aspects focus on maximizing tree diversity while producing and training component trees. Alternatively, a novel cognitive-inspired diversity-based random forests method, diversity-based random forests via sample weight learning (DRFS), is proposed. Given numerous component trees from the original random forests, DRFS selects and combines tree classifiers adaptively via diversity learning and sample weight learning. By designing a matrix for the data distribution creatively, a unified optimization model is formulated to learn and select diverse trees, where tree weights are learned through a convex quadratic programming problem with sample weights. Moreover, a self-training algorithm is proposed to solve the convex optimization iteratively and learn sample weights automatically. Comparative experiments on 39 typical UCI classification benchmarks and a variety of real-world text categorization benchmarks of our proposed method are conducted. Extensive experiments show that our method outperforms the traditional methods. Our proposed DRFS method can select and combine tree classifiers adaptively and improves the performance on a variety of classification tasks.

关键词： Diversity-based ensembles Classifier ensemble Random forests Sample weight learning convex quadratic programming

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Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method

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DISCRETE APPLIED MATHEMATICS 2009年第6期157卷 1185-1197页

作者： Billionnet, Alain Elloumi, Sourour Plateau, Marie-Christine Conservatoire Natl Arts & Metiers Lab CEDRIC F-75141 Paris France Inst Informat Entreprise Lab CEDRIC F-91025 Evry France

Let (QP) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear equality constraints. In this paper, we present QCR, a general method to reformulate (QP) into an equivalent 0-1 program with a convex quadratic objective function. The reformulated problem can then be efficiently solved by a classical branch-and-bound algorithm, based on continuous relaxation. This idea is already present in the literature and used in standard solvers such as CPLEX. Our objective in this work was to find a convex reformulation whose continuous relaxation bound is, moreover, as tight as possible. From this point of view, we show that QCR is optimal in a certain sense. State-of-the-art reformulation methods mainly operate a perturbation of the diagonal terms and are valid for any {0, 1} vector. The innovation of QCR comes from the fact that the reformulation also uses the equality constraints and is valid on the feasible solution domain only. Hence, the superiority of QCR holds by construction. However, reformulation by QCR requires the solution of a semidefinite program which can be costly from the running time point of view. We carry out a computational experience on three different combinatorial optimization problems showing that the costly Computational time of reformulation by QCR can however result in a drastically more efficient branch-and-bound phase. Moreover, our new approach is competitive with very specific methods applied to particular optimization problems. (C) 2008 Elsevier B.V. All rights reserved.

关键词： quadratic 0-1 programming convex quadratic programming Semidefinite programming Densest k-subgraph Graph bisection Task allocation Experiments

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A framework for coupled deformation-diffusion analysis with application to degradation/healing

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2012年第9期89卷 1144-1170页

作者： Mudunuru, M. K. Nakshatrala, K. B. Univ Houston Dept Civil & Environm Engn Houston TX 77204 USA

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformationdiffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework, we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always snon-negative, which is one of the main contributions of this paper. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： coupled deformation-diffusion analysis non-negative solutions maximum principles degradation healing damage mechanics convex quadratic programming staggered coupling algorithm

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A study on sensitivity analysis for convex quadratic programs

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2006年第4期23卷 439-452页

作者： Lim, Sungmook Korea Univ Coll Econ & Commerce Seoul 339700 South Korea

We extend the two similar interior-point approaches to sensitivity analysis originally developed for linear programs to those for convex quadratic programs, where the first approach is the e-sensitivity analysis and the other is Yildirim and Todd's. We study the relationship between the bounds on perturbation of the input parameters arising from the extension of Yildirim and Todd's approach and those from the E-sensitivity analysis. Furthermore, we prove that Yildirim and Todd's bounds are asymptotically the same as the symmetrized optimal tripartition bounds in the case of a special type of nondegeneracy.

关键词： convex quadratic programming sensitivity analysis interior-point method epsilon-sensitivity analysis

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