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Binary partitioning, perceptual grouping, and restoration with semidefinite programming

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2003年第11期25卷 1364-1379页

作者： Keuchel, J Schnörr, C Schellewald, C Cremers, D Univ Mannheim Dept Math & Comp Sci CVGPR Grp D-38131 Mannheim Germany

We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter-free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hyperplane technique. Apart from a symmetry condition, no assumptions (such as metric pairwise interactions) are made with respect to the objective criterion. As a consequence, the approach can be applied to a wide range of problems. Applications to unsupervised partitioning, figure-ground discrimination, and binary restoration are presented along with extensive ground-truth experiments. From the viewpoint of relaxation of the underlying combinatorial problem, we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds.

关键词： image partitioning segmentation graph cuts perceptual grouping figure-ground discrimination combinatorial optimization relaxation convex optimization convex programming

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Quadratic characterization and use of output stabilizable subspaces

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2003年第4期48卷 654-660页

作者： Castelan, EB Hennet, JC Villarreal, ERL Dept Automacao & Sistemas BR-88040900 Florianopolis SC Brazil CNRS LAAS F-31077 Toulouse 4 France

This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C, A, B)-invariant subspaces. The work provides a new characterization of output stabitizable (C, A, B)-invariant subspaces through two coupled quadratic stabilization conditions. An equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by, static output feedback. An algorithm is provided and numerical examples are reported to illustrate the approach.

关键词： convex programming geometric approach Lyapunov equations output feedback quadratic stabilizability

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Fault tolerant control and classification for longitudinal vehicle control

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JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 2003年第3期125卷 320-329页

作者： Song, B Hedrick, JK Howell, A Univ Calif Berkeley Berkeley CA 94720 USA

In this paper, a new method of analyzing for the performance loss caused by faults in the systems is presented, and applied to the design of a fault tolerant longitudinal controller for a transit bus. Based on the amount of performance loss measured by a quadratic function, fault impact assessment is developed for both single and multiple faults. More specifically, ellipsoidal approximation of the tracking error bounds via dynamic surface control (DSC) is obtained via convex optimization technique for the nonlinear closed-loop system. Relying on the fault impact to the closed loop system and its isolatability on a fault detection and diagnosis system, the fault classification is proposed to provide a switching logic in the framework of a switched hierarchical structure. Finally, simulation results of the fault tolerant controller and corresponding fault classification are shown for multiple multiplicative faults.

关键词： Errors Actuators road vehicles convex programming Brakes Closed loop systems pattern classification Vehicles Dynamics (Mechanics) Design nonlinear control systems Uncertainty fault tolerance closed loop systems Control equipment Engines

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On the convergence of conditional ε-subgradient methods for convex programs and convex-concave saddle-point problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第3期151卷 461-473页

作者： Larsson, T Patriksson, M Strömberg, AB Chalmers Univ Technol Dept Math SE-41296 Gothenburg Sweden Linkoping Univ Dept Math SE-58183 Linkoping Sweden Fraunhofer Chalmers Res Ctr Ind Math SE-41288 Gothenburg Sweden

The paper provides two contributions. First, we present new convergence results for conditional epsilon-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593;USSR Comput. Math. Math. Phys. 9 (1969) 14;Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. Program. 62 (1993) 261;Eur. J. Oper. Res. 88 (1996) 382;Math. Program. 81 (1998) 23] to a broader framework. Secondly, we establish the application of this technique to solve non-strictly convex-concave saddle point problems, such as primal-dual formulations of linear programs. Contrary to several previous solution algorithms for such problems, a saddle-point is generated by a very simple scheme in which one component is constructed by means of a conditional epsilon-subgradient algorithm, while the other is constructed by means of a weighted average of the (inexact) subproblem solutions generated within the subgradient method. The convergence result extends those of [Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin, 1985;Oper. Res. Lett. 19 (1996) 105;Math. Program. 86 (1999) 283] for Lagrangian saddle-point problems in linear and convex programming, and of [Int. J. Numer. Meth. Eng. 40 (1997) 1295] for a linear-quadratic saddle-point problem arising in topology optimization in contact mechanics. (C) 2002 Elsevier B.V. All rights reserved.

关键词： convex programming non-linear programming game theory large-scale optimization

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Upper semicontinuity of closed-convex-valued multifunctions

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2003年第3期57卷 409-425页

作者： Cánovas, MJ López, MA Ortega, EM Parra, J Miguel Hernandez Univ Elche Ctr Operat Res Alicante 03202 Spain Univ Alicante Dept Stat & Operat Res Alicante 03071 Spain

In this paper we study the (Berge) upper semicontinuity of a generic multifunction assigning to each parameter, in a metric space, a closed convex subset of the n-dimensional Euclidean space. A relevant particular case arises when we consider the feasible set mapping associated with a parametric family of convex semi-infinite programming problems. Related to such a generic multifunction, we introduce the concept of epsilon-reinforced mapping, which will allow us to establish a sufficient condition for the aimed property. This condition turns out to be also necessary in the case that the boundary of the image set at the nominal value of the parameter contains no half-lines. On the other hand, it is well-known that every closed convex set in the Euclidean space can be viewed as the solution set of a linear semi-infinite inequality system and, so, a parametric family of linear semi-infinite inequality systems can always be associated with the original multifunction. In this case, a different necessary condition is provided in terms of the coefficients of these linear systems. This condition tries to measure the relative variation of the right hand side with respect to the left hand side of the constraints of the systems in a neighbourhood of the nominal parameter.

关键词： stability multifunctions upper semicontinuity semi-infinite programming convex programming feasible set mapping

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A quasi-Newton penalty barrier method for convex minimization problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2003年第1期26卷 5-34页

作者： Armand, P Univ Limoges Fac Sci CNRS LACO F-87060 Limoges France

We describe an infeasible interior point algorithm for convex minimization problems. The method uses quasi-Newton techniques for approximating the second derivatives and providing superlinear convergence. We propose a new feasibility control of the iterates by introducing shift variables and by penalizing them in the barrier problem. We prove global convergence under standard conditions on the problem data, without any assumption on the behavior of the algorithm.

关键词： BFGS algorithm constrained optimization convex programming interior point method line search primal-dual method quasi-Newton method

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Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 2003年第2期50卷 294-297页

作者： Wu, CW IBM Corp Div Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA

There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analytical criteria for global or local synchronization. The second class of results relies on linearization around the synchronization manifold and the computation of Lyapunov exponents. The computation of Lyapunov exponents is mainly done via numerical experiments and can only show local synchronization in the neighborhood of the synchronization manifold. On the other hand, Lyapunov's direct method is more rigorous and can give global results. The coupling topology is generally expressed in matrix form and the first class of methods mainly deals with symmetric matrices whereas the second class of methods can work with all diagonalizable matrices. The purpose of this brief is to bridge the gap in the applicability of the two classes of methods by considering the nonsymmetric case-for the first class of methods. We derive a synchronization criterion for nonreciprocal coupling related to a numerical quantity that depends on the coupling topology and we present methods for computing this quantity.

关键词： chaos convex programming coupled oscillators Lyapunov exponents Lyapunov functions nonlinear programming nonreciprocal coupling synchronization

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An infeasible active set method for quadratic problems with simple bounds

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SIAM JOURNAL ON OPTIMIZATION 2003年第1期14卷 35-52页

作者： Kunisch, K Rendl, F Graz Univ Inst Math A-8010 Graz Austria Univ Klagenfurt Inst Math A-9020 Klagenfurt Austria

A primal-dual active set method for quadratic problems with bound constraints is presented. Based on a guess on the active set, a primal-dual pair (x, s) is computed that satisfies the first order optimality condition and the complementarity condition. If (x, s) is not feasible, a new active set is determined, and the process is iterated. Sufficient conditions for the iterations to stop in a finite number of steps with an optimal solution are provided. Computational experience indicates that this approach often requires only a few (less than 10) iterations to find the optimal solution.

关键词： primal-dual active set method convex programming

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On First Order Optimality Conditions for Vector Optimization

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 371-386页

作者： L.M.Gra■a Drummond A.N.Iusem B.F.Svaiter Programa de Engenharia de Sistemas de Computacao COPPE-UFRJCP 68511Rio de Janeiro-RJ21945970BrazilInstituto de Matematica Pura e Aplicada (IMPA) Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320BrazilInstituto de Matematica Pura e Aplicada (IMPA)Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320Brazil

We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presenting some well known existence results for these problems, based on a scalarization approach, we establish necessity of the optimality conditions under a Slater-like constraint qualification, and then sufficiency for the K-convex case. We present two alternative sets of optimality conditions, with the same properties in connection with necessity and sufficiency, but which are different with respect to the dimension of the spaces to which the dual multipliers belong. We introduce a duality scheme, with a point-to-set dual objective, for which strong duality holds. Some examples and open problems for future research are also presented.

关键词： Cone constraints vector optimization Pareto minimization first order optimality conditions convex programming duality

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Nonlinear proximal decomposition method for convex programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2000年第2期106卷 357-372页

作者： Kyono, M Fukushima, M Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto Japan Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto Japan

In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem.

关键词： nonlinear proximal decomposition method Bregman functions convex programming

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