Linearization techniques for $\mathbb {L}^{\infty }$See PDF-control problems and dynamic programming principles in classical and $\mathbb {L}^{\infty }$See PDF-control problems

Dan Goreac; Oana-Silvia Serea

Displaying similar documents to “Linearization techniques for $𝕃^{\infty}$ See PDF-control problems and dynamic programming principles in classical and $𝕃^{\infty}$ See PDF-control problems”

On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control $u(\cdot)$ . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control $u=u(\cdot)$ , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system $\Sigma$ , referred to a system $\chi$ of Lagrangian co-ordinates, and to try and write some handy...

Saddle point criteria for second order $η$ -approximated vector optimization problems

Anurag Jayswal, Shalini Jha, Sarita Choudhury (2016)

Kybernetika

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The purpose of this paper is to apply second order $η$ -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $η$ -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $η$ -saddle point and the second order $η$ -Lagrange function are defined for the second order $η$ -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution...

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

A localization property for $B_{p q}^{s}$ and $F_{p q}^{s}$ spaces

Hans Triebel (1994)

Studia Mathematica

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Let $f^{j} = \sum_{k} a_{k} f (2^{j + 1} x - 2 k)$ , where the sum is taken over the lattice of all points k in $ℝ^{n}$ having integer-valued components, j∈ℕ and $a_{k} \in ℂ$ . Let $A_{p q}^{s}$ be either $B_{p q}^{s}$ or $F_{p q}^{s}$ (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on $ℝ^{n} .$ The aim of the paper is to clarify under what conditions $∥ f^{j} | A_{p q}^{s} ∥$ is equivalent to $2^{j (s - n / p)} (\sum_{k} | a_{k} |^{p})^{1 / p} ∥ f | A_{p q}^{s} ∥$ .

Interior-point method for large-scale $l_{1}$ optimization

Lukšan, Ladislav, Matonoha, Ctirad, Vlček, Jan

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Transportation flow problems with Radon measure variables

Marcus Wagner (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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For a multidimensional control problem ${(P)}_{K}$ involving controls $u \in L_{\infty}$ , we construct a dual problem ${(D)}_{K}$ in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of $(L_{\infty}) *$ . For this purpose, we add to ${(P)}_{K}$ a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

Localization techniques in $L^{p}$ spaces

A. Pełczyński, H. Rosenthal (1975)

Studia Mathematica

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On control theory and its applications to certain problems for Lagrangian systems. On hyper-impulsive motions for these. III. Strengthening of the characterizations performed in parts I and II, for Lagrangian systems. An invariance property.

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In [1] I and II various equivalence theorems are proved; e.g. an ODE $(\mathcal{E})\dot{z}=F(t,z,u,\dot{u})\,(\in\mathbb{R}^{m})$ with a scalar control $u=u(\cdot)$ is linear w.r.t. $\dot{u}$ iff $(\alpha)$ its solution $z(u,\cdot)$ with given initial conditions (chosen arbitrarily) is continuous w.r.t. $u$ in a certain sense, or iff $(\beta)$ $z(u,\cdot)$ satisfies certain conditions by which $1^{st}$ -order discontinuities of $u$ and $\dot{u}$ can be treated satisfactorily. In the case when, for $z=(q,p)$ equation $(\mathcal{E})$ is a semi-Hamiltonian system, equivalent to a system of Lagrangian equations of a general type,...

Spaces of functions on domain $Ω$ , whose $k$ -th derivatives are measures defined on $\bar{Ω}$

Jiří Souček (1972)

Časopis pro pěstování matematiky

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$L_{p, q}$ spaces

Joseph Kupka

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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the $L_{p, q}$ spaces................................. 114. Integral representation of bounded linear functionals on $L_{p, q} (B)$ ........ 235. Examples in $L_{p, q}$ theory...................................................................................

$H^{\infty}$ calculus and dilatations

Andreas M. Fröhlich, Lutz Weis (2006)

Bulletin de la Société Mathématique de France

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We characterise the boundedness of the $H^{\infty}$ calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if $- A$ generates a bounded analytic $C_{0}$ semigroup $(T_{t})$ on a UMD space, then the $H^{\infty}$ calculus of $A$ is bounded if and only if $(T_{t})$ has a dilation to a bounded group on $L^{2} ([0, 1], X)$ . This generalises a Hilbert space result of C.LeMerdy. If $X$ is an $L^{p}$ space we can choose another $L^{p}$ space in place of $L^{2} ([0, 1], X)$ .