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Alkulaibi; On existence of monotone solutions for secondorder nonconvex differential inclusions in infinite dimensional spaces
 Portugalies Mathematica
"... Abstract: This paper is concerned with the existence of monotone solutions in an in¯nite dimensional Hilbert space for a second order di®erential inclusion and without the assumption of the convexity. 1 ..."
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Cited by 2 (1 self)
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Abstract: This paper is concerned with the existence of monotone solutions in an in¯nite dimensional Hilbert space for a second order di®erential inclusion and without the assumption of the convexity. 1
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Basic objects in natural categories
 COGNITIVE PSYCHOLOGY
, 1976
"... Categorizations which humans make of the concrete world are not arbitrary but highly determined. In taxonomies of concrete objects, there is one level of abstraction at which the most basic category cuts are made. Basic categories are those which carry the most information, possess the highest categ ..."
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Cited by 892 (1 self)
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category cue validity, and are, thus, the most differentiated from one another. The four experiments of Part I define basic objects by demonstrating that in taxonomies of common concrete nouns in English based on class inclusion, basic objects are the most inclusive categories whose members: (a) possess
Differential inclusions
, 1984
"... disordered breathing in a cohort of patients with sporadic ..."
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Cited by 326 (0 self)
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disordered breathing in a cohort of patients with sporadic
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
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Cited by 445 (31 self)
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that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadraticallyconstrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 365 (5 self)
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and the onenorm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a rootfinding algorithm for finding arbitrary points
NONCONVEX RANDOM DIFFERENTIAL INCLUSION
"... Abstract: In this paper, I prove the existence of random solution for the first order initial value problem of nonconvex random differential inclusion through random fixed point theory. ..."
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Abstract: In this paper, I prove the existence of random solution for the first order initial value problem of nonconvex random differential inclusion through random fixed point theory.
Nonmonotone spectral projected gradient methods on convex sets
 SIAM Journal on Optimization
, 2000
"... Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone lin ..."
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Cited by 215 (28 self)
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Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone
Convex equations and differential inclusions in hybrid systems
 In 43rd IEEE Conference on Decision and Control
, 2004
"... Abstract — Differential equations with discontinuous right hand sides enable modeling and analysis of control systems with switching elements at a high level of abstraction. Solutions of these differential equations are based on the Filippov, Utkin or similar solution concepts. These solution concep ..."
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Cited by 3 (3 self)
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concepts are in general inconvenient for modeling and verification using formal languages, because they lead to ambiguities in differential algebraic equations. This paper introduces convex equations to avoid such ambiguities in formal languages. Convex equations integrate the functionality of the Filippov
Non convex problems of the calculus of variations and differential inclusions
 TO APPEAR IN HANDBOOK OF DIFFERENTIAL EQUATIONS (STATIONARY PARTIAL DIFFERENTIAL EQUATIONS),
, 2005
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Results 1  10
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