Publications related to Norm (mathematics)

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares ...

MATHICSE2018

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

In this paper, we consider the problem of sequentially optimizing a black-box function

f

based on noisy samples and bandit feedback. We assume that

f

is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yield ...

2017

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Volkan Cevher, Ya-Ping Hsieh, Marwa El Halabi, Cong Bang Vu, Van Quang Nguyen

In this paper, we consider composite convex minimization problems. We advocate the merit of considering Generalized Proximal gradient Methods (GPM) where the norm employed is not Euclidean. To that end, we show the tractability of the general proximity ope ...

2017

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Colin Neil Jones, Milan Korda

We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates polynomial under-approximations to the value function of the optimal ...

Elsevier Science Bv2017

Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward

Michael Christoph Gastpar, Saeid Sahraei

A particular instance of the shortest vector problem (SVP) appears in the context of compute-and-forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order O(nψlog(nψ)) , where ψ=sqrt(P ||h||^2+1) ...

Institute of Electrical and Electronics Engineers2017

Small subset sums

Gergely Ambrus

Let parallel to.parallel to be a norm in R-d whose unit ball is B. Assume that V subset of B is a finite set of cardinality n, with Sigma(v is an element of V) v = 0. We show that for every integer k with 0

Elsevier Science Inc2016

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory ...

World Scientific Publ Co Pte Ltd2016

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

Assyr Abdulle, Martin Ernst Huber

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then deri ...

Wiley-Blackwell2016

Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization

Ali H. Sayed, Roula Nassif

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entri ...

IEEE2016

Fixed-structure LPV Discrete-time Controller Design with Induced l2-Norm and H2 Performance

Alireza Karimi, Zlatko Emedi

A new method for the design of fixed-structure dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, $\mathscr{H} ...

2015

Norm (mathematics)

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MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward

Small subset sums

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization

Fixed-structure LPV Discrete-time Controller Design with Induced l2-Norm and H2 Performance

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Fixed-structure LPV Discrete-time Controller Design with Induced l2-Norm and H2 Performance

Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward

Small subset sums

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization