Results 1  10
of
110
A generalized Gaussian image model for edgepreserving MAP estimation
 IEEE Trans. on Image Processing
, 1993
"... Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distri ..."
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Cited by 238 (34 self)
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Absfrucf We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisifies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the U posteriori loglikeihood function. The GGMRF is demonstrated to be useful for image reconstruction in lowdosage transmission tomography. I.
Applications of Secondorder Cone Programming;
"... In a secondorder cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of secondorder (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than semidefin ..."
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Cited by 154 (11 self)
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In a secondorder cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of secondorder (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than semidefinite programs (SDPs). Several efficient primaldual interiorpoint methods for SOCP have been developed in the last few years.
Multiobjective output feedback control via LMI
 in Proc. Amer. Contr. Conf
, 1997
"... The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms. ..."
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Cited by 72 (5 self)
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The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms. Suboptimal solutions are computed using finite dimensional Qparametrization. The objective value of the suboptimal Q's converges to the true optimum as the dimension of Q is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea [11] for the H2 case. A simple example computed using FIR (Finite Impulse Response) Q's is presented.
Method of centers for minimizing generalized eigenvalues
 Linear Algebra Appl
, 1993
"... We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear specialized, it is in fact quite general, and includes for example all linear, quadratic, and linear fr ..."
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Cited by 65 (14 self)
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We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear specialized, it is in fact quite general, and includes for example all linear, quadratic, and linear fractional programs. Many problems arising in control theory can be cast in this form. The problem is nondifferentiable but quasiconvex, so methods such as Kelley's cuttingplane algorithm or the ellipsoid algorithm of Shor, Nemirovksy, and Yudin are guaranteed to minimize it. In this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently. The algorithm is a variation on Huard's method of centers, using a selfconcordant barrier for matrix inequalities developed by Nesterov and Nemirovsky. (Nesterov and Nemirovsky have also extended their potential reduction methods to handle the same problem [NN91b].) Since the problem is quasiconvex but not convex, devising a nonheuristic stopping criterion (i.e., one that guarantees a given accuracy) is more difficult than in the convex case. We describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper, in some cases, than a more general result due to Nesterov and Nemirovsky. The algorithm is demonstrated on an example: determining the quadratic Lyapunov function that optimizes a decay rate estimate for a differential inclusion.
Optimization over state feedback policies for robust control with constraints
, 2005
"... This paper is concerned with the optimal control of linear discretetime systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is e ..."
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Cited by 30 (4 self)
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This paper is concerned with the optimal control of linear discretetime systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This result implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods without having to introduce any conservatism in the problem formulation. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closedloop system is inputtostate stable (ISS) and the constraints are satisfied for all time and for all allowable disturbance sequences. The cost that is chosen to be minimized in the associated finite horizon optimal control problem is a quadratic function in the disturbancefree state and input sequences. It is shown that the value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic or given by a 1norm or ∞norm bound, or a secondorder cone program (SOCP) if the disturbance set is ellipsoidal or given by a 2norm bound.
Bayesian Estimation of Transmission Tomograms Using Segmentation Based Optimization
 IEEE Trans. on Nuclear Science
, 1992
"... We present a method for nondifferentiable optimization in MAP estimation of computed transmission tomograms. This problem arises in the application of a Markov random field image model with absolute value potential functions. Even though the required optimization is on a convex function, local optim ..."
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Cited by 29 (7 self)
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We present a method for nondifferentiable optimization in MAP estimation of computed transmission tomograms. This problem arises in the application of a Markov random field image model with absolute value potential functions. Even though the required optimization is on a convex function, local optimization methods, which iteratively update pixel values, become trapped on the nondifferentiable edges of the function. We propose an algorithm which circumvents this problem, by updating connected groups of pixels formed in an intermediate segmentation step. Experimental results show that this approach substantially increases the rate of converge and the quality of the reconstruction.
On Finite Gain Stabilizability of Linear Systems Subject to Input Saturation
 SIAM J. Control and Optimization
, 1993
"... This paper deals with (global) finitegain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every L ..."
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Cited by 25 (9 self)
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This paper deals with (global) finitegain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every L
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
"... ..."
Semidefinite Programming Duality and Linear TimeInvariant Systems
, 2003
"... Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to Linear Matrix Inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs as well as dual opt ..."
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Cited by 21 (2 self)
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Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to Linear Matrix Inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs as well as dual optimization problems can be formulated. These can in turn be reinterpreted in control or system theoretic terms, often yielding new results or new proofs for existing results from control theory. We explore such connections for a few problems associated with linear timeinvariant systems. 1
Controller design via nonsmooth multidirectional search
 SIAM J. Control Optim
, 2006
"... z Abstract We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixedorder output feedback controller design, simultaneous stabilization, H2=H1 synthesis and muc ..."
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Cited by 21 (13 self)
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z Abstract We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixedorder output feedback controller design, simultaneous stabilization, H2=H1 synthesis and much else. We show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness. Our technique is the most efficient when small controllers for plants with large state dimension are sought. Our numerical testing includes several benchmark examples. For instance, our algorithm needs 0.41 seconds to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem [22], a system with 55 states. The first static controller without performance specifications for this system was obtained in [16]. Keywords: N Phard design problems, static output feedback, fixedorder synthesis, simultaneous stabilization, mixed H2=H1synthesis, pattern search algorithm, moving polytope, nonsmooth analysis, spectral bundle method, "gradients, bilinear matrix inequality (BMI).