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81
Scaling MPE Inference for Constrained Continuous Markov Random Fields with Consensus Optimization
"... Probabilistic graphical models are powerful tools for analyzing constrained, continuous domains. However, finding most-probable explanations (MPEs) in these models can be computationally expensive. In this paper, we improve the scalability of MPE inference in a class of graphical models with piecewi ..."
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Cited by 17 (14 self)
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with piecewise-linear and piecewise-quadratic dependencies and linear constraints over continuous domains. We derive algorithms based on a consensus-optimization framework and demonstrate their superior performance over state of the art. We show empirically that in a large-scale voter-preference modeling problem
Automatic Synthesis of Piecewise Linear Quadratic Invariants for Programs?
"... Abstract. Among the various critical systems that worth to be for-mally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com-putations update internal states and produce commands to update the system state. Those sy ..."
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Cited by 1 (0 self)
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systems are yet hardly analyzable by available static analysis method, since, even if performing mainly linear computations, the computation of a safe set of reachable states often requires quadratic invariants. In this paper we consider the general setting of a piecewise affine pro-gram; that is a
An L2-Gain Analysis of Piecewise Affine Systems by Piecewise Quadratic Storage Functions
"... Abstract — Piecewise affine (PWA) systems, which belong to a class of hybrid systems receiving a lot of attention, are useful for describing dynamics of real-world systems. A PWA system, whose dynamic is composed of a finite number of affine dynamics and switching laws, is at an advantage because ex ..."
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existing analysis and control methods for linear systems may be applied to the system with a little modification. Based on this concept, in existing literature, some analysis conditions via piecewise quadratic functions were suggested for PWA systems whose switchings of dynamics depend only on their states
Exponential Stability Of Hybrid Systems Using Piecewise Quadratic Lyapunov Functions Resulting In Lmis
- in LMIs” Proc. 14 th Triennial World Congress
, 1999
"... : Exponential stability of hybrid systems using a Lyapunov approach is considered in this paper. The continuous part of the hybrid system is described by nonlinear differential equations that depend on a discrete state. The discrete state changes when certain switch sets are reached. By using piecew ..."
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Cited by 9 (0 self)
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piecewise quadratic forms of the Lyapunov function candidates, it is shown how the stability conditions can be formulated as linear matrix inequalities (LMIs) and a nonlinear optimization problem. An example illustrates the method. Copyright c fl1999 IFAC Keywords: Hybrid Systems, Exponential Stability
Stability criteria for switched and hybrid systems
- SIAM Review
, 2007
"... The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, an ..."
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Cited by 114 (8 self)
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inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent
The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients
, 1998
"... A standard system of interval linear equations is defined as Ax = b, where A is an m × n coefficient matrix with (compact) intervals as entries, and b is an m-dimensional vector whose components are compact intervals. It is known that for systems of interval linear equations the solution s ..."
Abstract
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Cited by 8 (6 self)
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allow only symmetric matrices A (a ij = a ji ), then the corresponding solution set becomes (in general) piecewise-quadratic.
DISCRETIZATION OF ELLIPTIC CONTROL PROBLEMS WITH TIME DEPENDENT PARAMETERS
"... Abstract. We consider linear-quadratic problems of optimal control with an elliptic state equation and control constraints. For a discretization of the state equation by the method of Finite Differences and a piecewise approximation of the control we develop error estimates for the solution of the d ..."
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Abstract. We consider linear-quadratic problems of optimal control with an elliptic state equation and control constraints. For a discretization of the state equation by the method of Finite Differences and a piecewise approximation of the control we develop error estimates for the solution
On the Complexity of Time-Dependent Shortest Paths
"... We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomial-size) piecewise line ..."
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Cited by 4 (0 self)
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We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomial-size) piecewise
L_p Optimal d Dimensional Triangulations for Piecewise Linear Interpolation: A New Result on Data dependent Triangulations
, 1993
"... In this paper we address the problem of optimum piecewise linear approximation of general quadratic functions in R e for d >= 2. In particular the problem is posed as follows: Given a quadratic function f : R e ) R of the form f(x) = x'Ax + b'x + c, where matrix A symmetric and positi ..."
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Cited by 5 (0 self)
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In this paper we address the problem of optimum piecewise linear approximation of general quadratic functions in R e for d >= 2. In particular the problem is posed as follows: Given a quadratic function f : R e ) R of the form f(x) = x'Ax + b'x + c, where matrix A symmetric
An efficient algorithm for image segmentation, Markov random fields and related problems
- Journal of the ACM
, 2001
"... Abstract. Problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements, or order constraints. In such problems, the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modi ..."
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Cited by 50 (13 self)
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the deviation cost function is linear, quadratic or piecewise linear convex with few pieces (where “few” means a number exponential in a polynomial function of the number of variables and constraints).
Results 1 - 10
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81
