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CONVEX ANALYSIS AND SPECTRAL ANALYSIS OF TIMED EVENT GRAPHS
, 2016
"... Convex analysis and spectral analysis of timed event graphs ..."
Hyperbolic Polynomials and Convex Analysis
, 1998
"... Abstract. A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t ↦ → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, G˚arding proved in 1951 that the largest such root is a convex function of x, and s ..."
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Cited by 39 (4 self)
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Abstract. A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t ↦ → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, G˚arding proved in 1951 that the largest such root is a convex function of x
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We
Robust principal component analysis?
 Journal of the ACM,
, 2011
"... Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the ..."
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Cited by 564 (26 self)
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rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the 1 norm. This suggests the possibility of a principled approach to robust principal component
Nonlinear Analysis and Convex Analysis,
, 2000
"... ” Conjugate points ” is a global concept in calculus of variation, and plays an important role in discussing optimality. Though it has been a theme of differential geometry, mathematical programming approach has been recently developed with several extensions of the conjugate points theory to optim ..."
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” Conjugate points ” is a global concept in calculus of variation, and plays an important role in discussing optimality. Though it has been a theme of differential geometry, mathematical programming approach has been recently developed with several extensions of the conjugate points theory to optimal control problems and variational problems with state constraints. In these extremal problems, the variable is not a vector $x $ in $R^{n} $ but a function $x(t) $. So a simple and natural question arises. Is it possible to establish a conjugate points theory for a minimization problem: minimize $f(x) $ on $x\in R^{n}$? In [3], the author positively answered this question. He introduced ”the Jacobi equation” and ”conjugate points ” for it, and describe optimality conditions in terms of”conjugate points”. In this paper, we extend it to a constrained nonlinear programming. 1. Jacobi’s conjugate points theory In this section, we review the classical conjugate points theory for the simplest problem in calculus of variations: $(SP) $ Minimize $\int_{0}^{T}f(t, x(t),\dot{X}(t))dt$ subject to $x(\mathrm{O})=A, $ $x(T)=B $.
LOGARITHMIC FUNCTIONAL MEAN IN CONVEX ANALYSIS
"... ABSTRACT. In this paper, we present various functional means in the sense of convex analysis. In particular, a logarithmic mean involving convex functionals, extending the scalar one, is introduced. In the quadratic case, our functional approach implies immediately that of positive operators. Some e ..."
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Cited by 1 (0 self)
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ABSTRACT. In this paper, we present various functional means in the sense of convex analysis. In particular, a logarithmic mean involving convex functionals, extending the scalar one, is introduced. In the quadratic case, our functional approach implies immediately that of positive operators. Some
Applications of Convex Analysis within Mathematics
, 2013
"... In this paper, we study convex analysis and its theoretical applications. We apply important tools of convex analysis to Optimization and to Analysis. Then we show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we rec ..."
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Cited by 1 (1 self)
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In this paper, we study convex analysis and its theoretical applications. We apply important tools of convex analysis to Optimization and to Analysis. Then we show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we
Applications of convex analysis to multidimensional scaling
 Recent Developments in Statistics
, 1977
"... Abstract. In this paper we discuss the convergence of an algorithm for metric and nonmetric multidimensional scaling that is very similar to the Cmatrix algorithm of Guttman. The paper improves some earlier results in two respects. In the first place the analysis is extended to cover general Minkov ..."
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Cited by 73 (5 self)
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Abstract. In this paper we discuss the convergence of an algorithm for metric and nonmetric multidimensional scaling that is very similar to the Cmatrix algorithm of Guttman. The paper improves some earlier results in two respects. In the first place the analysis is extended to cover general
Convexity analysis and splitting algorithm for the . . .
, 2010
"... We consider the dynamic spectrum management (DSM) system in which many users share the same frequency band and it is divided into multiple tones. In such a system, each user or central office allocates the transmission power to each tone adaptively in response to channel conditions. However, if mult ..."
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We consider the dynamic spectrum management (DSM) system in which many users share the same frequency band and it is divided into multiple tones. In such a system, each user or central office allocates the transmission power to each tone adaptively in response to channel conditions. However, if multiple users allocate their transmission powers to the same tone, then their data rate may decrease due to the electromagnetic interference called crosstalk. Therefore, it is required to allocate the transmission power so that every user can achieve a sufficient data rate. Although the sumrate (the sum of all users ’ data rates) is the most typical measure of overall system performance, it is nonconcave in general, and hence, the sumrate maximization problem may have multiple local maxima. Thus, the algorithms that have been proposed so far could find nothing more than a “nearoptimal” solution under general conditions. In this paper, we provide conditions under which the sumrate function is guaranteed to be concave over the feasible region. Moreover, by utilizing the concavity, we propose some splitting algorithms that can be implemented in a distributed manner. From the numerical experiments, we observe that the splitting algorithms solve the sumrate maximization problems efficiently.
Results 11  20
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226,466