Documents  90C25 | enregistrements trouvés : 37

- xiii, 279 p.
ISBN 978-3-642-11338-3

Lecture notes in mathematics , 1989

Localisation : Collection 1er étage

optimisation # programmation non-linéaire # problème quadratique

90C30 ; 90C26 ; 90C25 ; 90C55

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- 289 p.
ISBN 978-0-8218-2167-1

C.M.S. conference proceedings , 0027

Localisation : Collection 1er étage

théorie des nombres # analyse numérique # calcul de variation # optimisation # analyse non-linéaire # analyse constructive # fonction de Lyapunov # algorithme # calcul formel # calcul numérique # théorie du contrôle

11Y16 ; 11J70 ; 11Y65 ; 35J20 ; 41A65 ; 44A12 ; 46B20 ; 47A15 ; 49J52 ; 49K24 ; 58C20 ; 65K10 ; 90C25 ; 90C48

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ISBN 978-3-540-57624-2

Lecture notes in economics and mathematical systems , 0405

Localisation : Colloque 1er étage (PECS)

application monotone généralisée # convexité généralisée # fonction convexe généralisée # optimalité et dualité # programmation fractionnaire # programmation multi-objectif # programmation quasi-convexe

52A41 ; 52Axx ; 90C25 ; 90C26 ; 90C29

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Research talks;Computer Science;Control Theory and Optimization;Probability and Statistics

Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are $O(1/\sqrt{n})$ for general convex functions and reaches $O(1/n)$ for strongly-convex functions. In this tutorial, I will first present the classical results in stochastic approximation and relate them to classical optimization and statistics results. I will then show how the smoothness of loss functions may be used to design novel algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-based stochastic approximation algorithm leads to a convergence rate of $O(1/n)$ without strong convexity assumptions, while in the practical finite-data setting, an appropriate combination of batch and online algorithms leads to unexpected behaviors, such as a linear convergence rate for strongly convex problems, with an iteration cost similar to stochastic gradient descent. Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes ...

62L20 ; 68T05 ; 90C06 ; 90C25

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Research talks;Computer Science;Control Theory and Optimization;Probability and Statistics

Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are $O(1/\sqrt{n})$ for general convex functions and reaches $O(1/n)$ for strongly-convex functions. In this tutorial, I will first present the classical results in stochastic approximation and relate them to classical optimization and statistics results. I will then show how the smoothness of loss functions may be used to design novel algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-based stochastic approximation algorithm leads to a convergence rate of $O(1/n)$ without strong convexity assumptions, while in the practical finite-data setting, an appropriate combination of batch and online algorithms leads to unexpected behaviors, such as a linear convergence rate for strongly convex problems, with an iteration cost similar to stochastic gradient descent. Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes ...

62L20 ; 68T05 ; 90C06 ; 90C25

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Special events;30 Years of Wavelets;Analysis and its Applications;Probability and Statistics

One of the important "products" of wavelet theory consists in the insight that it is often beneficial to consider sparsity in signal processing applications. In fact, wavelet compression relies on the fact that wavelet expansions of real-world signals and images are usually sparse. Compressive sensing builds on sparsity and tells us that sparse signals (expansions) can be recovered from incomplete linear measurements (samples) efficiently. This finding triggered an enormous research activity in recent years both in signal processing applications as well as their mathematical foundations. The present talk discusses connections of compressive sensing and time-frequency analysis (the sister of wavelet theory). In particular, we give on overview on recent results on compressive sensing with time-frequency structured random matrices.

Keywords: compressive sensing - time-frequency analysis - wavelets - sparsity - random matrices - $\ell_1$-minimization - radar - wireless communications One of the important "products" of wavelet theory consists in the insight that it is often beneficial to consider sparsity in signal processing applications. In fact, wavelet compression relies on the fact that wavelet expansions of real-world signals and images are usually sparse. Compressive sensing builds on sparsity and tells us that sparse signals (expansions) can be recovered from incomplete linear measurements (samples) efficiently. This ...

94A20 ; 94A08 ; 42C40 ; 60B20 ; 90C25

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- viii; 185 p.
ISBN 978-3-11-036103-2

Series in nonlinear analysis and applications , 0022

Localisation : Ouvrage RdC (BACA)

espace de Hadamard # convexité # géodésique # matrice d'Hadamard # G-espace # espace métrique # optimisation convexe

47H20 ; 49M20 ; 49M25 ; 49M27 ; 51F99 ; 52A01 ; 60B99 ; 60J10 ; 92D15 ; 90-02 ; 90C48 ; 90C25 ; 90C30

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- xx; 347 p.
ISBN 978-1-4822-2207-4

Localisation : Ouvrage RdC (ALME)

théorie du point fixe # optimisation mathématique # analyse variationnelle # analyse convexe # analyse quasi-convexe # inégalités variationnelles # optimisation vectorielle # optimisation combinatoire multiobjectif

90-06 ; 90C25 ; 90C29 ; 90C27 ; 49J40 ; 49J53 ; 54C60 ; 54H25 ; 47H10 ; 26B25 ; 00B15

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- xxi; 654 p.
ISBN 978-0-7923-7771-9

International series in operations research & management science

Localisation : Ouvrage RdC (HAND)

programmation linéaire # optimisation mathématique # algorithmes

90-00 ; 90C22 ; 90C25 ; 49M37

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- xxi; 361p.
ISBN 978-1-84816-445-1

Imperial college press optimization series , 0001

Localisation : Ouvrage RdC (LASS)

problème de moments # équation polynomiale # optimisation mathématique # ensemble semi-algébrique # programmation semi-définie # programmation convexe # emsemble semi-algébrique # optimisation globale # équilibre de Nash # chaîne de Markov # système d'équations polynomiales

90-02 ; 90C22 ; 90C25 ; 78M05 ; 14P10

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- xvi; 298 p.
ISBN 978-3-642-30900-7

Lecture notes in mathematics , 2057

Localisation : Collection 1er étage

point fixe # espace de Hilbert # méthode itérative # opérateur # itération # théorème du point fixe

47-02 ; 49-02 ; 65-02 ; 90-02 ; 47H09 ; 47J25 ; 37C25 ; 65F10 ; 90C25 ; 47H10 ; 54H25

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- 235-616

Variational analysis, optimization, optimal control and applications , 0018

Localisation : Ouvrage RdC (SET)

90C25 ; 90C26 ; 47H05 ; 49Jxx ; 49Nxx ; 94Axx

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- xvi; 468 p.
ISBN 978-1-4419-9466-0

CMS books in mathematics

Localisation : Ouvrage RdC (BAUS)

analyse mathématique # espace de Hilbert # opérateur monotone # convexité # fonction convexe # programmation convexe # programmation non-linéaire # opérateur monotone # optimisation # approximation abstraite

41A50 ; 46-01 ; 46-02 ; 46Cxx ; 46C05 ; 47-01 ; 47-02 ; 47H05 ; 47H09 ; 47H10 ; 90-01 ; 90-02 ; 26A51 ; 26B25 ; 46N10 ; 47H04 ; 47N10 ; 52A05 ; 52A41 ; 65K05 ; 65K10 ; 90C25 ; 90C30

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- x; 219 p.
ISBN 978-0-8218-3352-0

Fields institute monographs , 0027

Localisation : Collection 1er étage

programmation semidéfinie # optmisation combinatoire # optimisation combinatoire # inégalité linéaire de matrices # géométrie convexe

90C22 ; 90C27 ; 15A39 ; 52A41 ; 65Y20 ; 90C05 ; 90C25 ; 90C51 ; 68Q25

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- xviii; 439 p.
ISBN 978-0-387-34431-7

Graduate texts in mathematics , 0258

Localisation : Collection 1er étage

programmation mathématique # optimisation mathématique

90-01 ; 90C30 ; 90C46 ; 90C25 ; 90C05 ; 90C20 ; 90C34 ; 90C47 ; 49M37 ; 49N15 ; 49J53 ; 49J50 ; 49M15 ; 49K35 ; 65K05 ; 65K10 ; 52A05 ; 52A07 ; 52A35 ; 52A41 ; 52A40 ; 52A37 ; 90Cxx

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- vi; 345 p.
ISBN 978-3-7643-8922-2

International series of numerical mathematics , 0158

Localisation : Ouvrage RdC (OPTI)

contrôle optimal # EDP # feedback

49-XX ; 35-XX ; 14J70 ; 26A16 ; 30F45 ; 35A15 ; 35B37 ; 35Bxx ; 35D05 ; 35J85 ; 35L05 ; 35L55 ; 35L99 ; 35Q30 ; 35Q35 ; 35Q40 ; 47J40 ; 49J20 ; 65J15 ; 65K10 ; 49K20 ; 49L20 ; 65N15 ; 49Q10 ; 70k70 ; 73K12 ; 74B05 ; 74K20 ; 74K25 ; 74K30 ; 74P05 ; 76D05 ; 76D07 ; 76N10 ; 76N15 ; 78A55 ; 80A20 ; 90C22 ; 90C25 ; 90C31 ; 90C90 ; 93A30 ; 93B05 ; 93B12 ; 93C20 ; 93D20 ; 93-XX ; 76D55 ; 35J65 ; 93B07

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- x, 266 p.
ISBN 978-3-540-78561-3

Nonconvex optimization and its applications , 0088

Localisation : Ouvrage RdC (MISH)

optimisation # programmation multiobjectif # fonction invexe # pseudolinéarité # dualité

90-02 ; 90C25

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- 310 p.
ISBN 978-0-387-29570-1

CMS Books in mathematics

Localisation : Ouvrage RdC (BORW)

fonction convexe # optimisation # théorie non-linéaire # calcul de variations # point intérieur # programmation convexe # dualité de Frenckel # théorème de Karush-Kuhn-Tucker # point fixe # théorème de Radenacker

90-01 ; 49-01 ; 90C51 ; 90C25 ; 49J53 ; 52A41 ; 46N10 ; 47H10

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- 405 p.
ISBN 978-0-89871-515-6

SIAM studies in applied and numerical mathematics , 0013

Localisation : Ouvrage RdC (NEST

programmation convexe # méthode du point intérieur # optimisation convexe # inégalité variationnelle # accélération de Karmakar # algorithme de Newton # auto-concordance

90C25 ; 90-02

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