Journal of Functional Analysis, ISSN 0022-1236, 05/2019, Volume 276, Issue 10, pp. 3226 - 3260

Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on c0(Γ) can be approximated uniformly on bounded sets by polyhedral...

Renorming | Polyhedrality | Approximation | Smoothness | MATHEMATICS | POLYHEDRAL APPROXIMATION | SMOOTH APPROXIMATIONS

Renorming | Polyhedrality | Approximation | Smoothness | MATHEMATICS | POLYHEDRAL APPROXIMATION | SMOOTH APPROXIMATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1272 - 1284

We prove that in every separable Banach space X with a Schauder basis and a Ck-smooth norm it is possible to approximate, uniformly on bounded sets, every...

Renorming | Fréchet smooth | [formula omitted]-smooth norm | Implicit function theorem | Approximation of norms | Minkowski functional | smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | POLYHEDRAL APPROXIMATION | NORMS | C-k-smooth norm | Frechet smooth | Electrical engineering

Renorming | Fréchet smooth | [formula omitted]-smooth norm | Implicit function theorem | Approximation of norms | Minkowski functional | smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | POLYHEDRAL APPROXIMATION | NORMS | C-k-smooth norm | Frechet smooth | Electrical engineering

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2012, Volume 22, Issue 4, pp. 1206 - 1223

We are concerned with linearly constrained convex programs with polyhedral norm as objective function. Friedlander and Tseng [SIAM J. Optim., 18 (2007), pp....

Exact regularization | Polyhedral norm | Duality mapping | Shrinkage | Sparsity | SPARSE REPRESENTATIONS | MATHEMATICS, APPLIED | polyhedral norm | duality mapping | THRESHOLDING ALGORITHM | EQUATIONS | CONVERGENCE | exact regularization | sparsity | shrinkage | Thresholds | Mathematical analysis | Norms | Mapping | Mathematical models | Regularization | Optimization

Exact regularization | Polyhedral norm | Duality mapping | Shrinkage | Sparsity | SPARSE REPRESENTATIONS | MATHEMATICS, APPLIED | polyhedral norm | duality mapping | THRESHOLDING ALGORITHM | EQUATIONS | CONVERGENCE | exact regularization | sparsity | shrinkage | Thresholds | Mathematical analysis | Norms | Mapping | Mathematical models | Regularization | Optimization

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 9/2015, Volume 54, Issue 2, pp. 390 - 411

We characterise finite and infinitesimal rigidity for bar-joint frameworks in $${\mathbb {R}}^d$$ R d with respect to polyhedral norms (i.e. norms with closed...

Polyhedral norm | 52A21 | Computational Mathematics and Numerical Analysis | 52B12 | Laman’s theorem | Infinitesimally rigid | Mathematics | 52C25 | Combinatorics | Bar-joint framework | Laman's theorem | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | FRAMEWORKS | Geometry | Theorems | Equivalence | Analogue | Placement | Mathematical analysis | Norms | Texts | Graph theory | Rigidity

Polyhedral norm | 52A21 | Computational Mathematics and Numerical Analysis | 52B12 | Laman’s theorem | Infinitesimally rigid | Mathematics | 52C25 | Combinatorics | Bar-joint framework | Laman's theorem | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | FRAMEWORKS | Geometry | Theorems | Equivalence | Analogue | Placement | Mathematical analysis | Norms | Texts | Graph theory | Rigidity

Journal Article

5.
Full Text
On the Solution Uniqueness Characterization in the L1 Norm and Polyhedral Gauge Recovery

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2017, Volume 172, Issue 1, pp. 70 - 101

This paper first proposes another proof of the necessary and sufficient conditions of solution uniqueness in 1-norm minimization given recently by H. Zhang, W....

65K05 | Mathematics | Theory of Computation | Minkowski function | Basis pursuit | 90C05 | Optimization | Optimality conditions | Sharp minimum | 90C46 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Solution existence and uniqueness | L1 minimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Convex polyhedral function | Gauge recovery | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | PROPERTY | SIGNAL RECOVERY | ATOMIC DECOMPOSITION | L-RECOVERY | L MINIMIZATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNCERTAINTY PRINCIPLES | DUALITY | SHARP | OPTIMIZATION | Algebra | Studies | Polyhedra | Uniqueness | Norms | Mathematical models | Polynomials | Gages | Recovery | Gauges | Optimization and Control

65K05 | Mathematics | Theory of Computation | Minkowski function | Basis pursuit | 90C05 | Optimization | Optimality conditions | Sharp minimum | 90C46 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Solution existence and uniqueness | L1 minimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Convex polyhedral function | Gauge recovery | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | PROPERTY | SIGNAL RECOVERY | ATOMIC DECOMPOSITION | L-RECOVERY | L MINIMIZATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNCERTAINTY PRINCIPLES | DUALITY | SHARP | OPTIMIZATION | Algebra | Studies | Polyhedra | Uniqueness | Norms | Mathematical models | Polynomials | Gages | Recovery | Gauges | Optimization and Control

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 2, pp. 1262 - 1272

We show that norms on certain Banach spaces X can be approximated uniformly, and with arbitrary precision, on bounded subsets of X by C∞ smooth norms and...

Renorming | James boundary | Polyhedral norm | Smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-BODIES | NORMS

Renorming | James boundary | Polyhedral norm | Smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-BODIES | NORMS

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 12/2017, Volume 68, Issue 3, pp. 661 - 669

The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the...

6 Data source | c02 - Mathematical Methods | Polyhedral norm | Single facility location problem | 2 International | 1-median | ORDERED MEDIAN PROBLEMS | Single facility location proble | Exact algorithm | Rectilinear norm | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Algorithms | Industrial locations | Demand | Operations research | Production planning | Site selection | Norms | Disks | Combinatorial analysis

6 Data source | c02 - Mathematical Methods | Polyhedral norm | Single facility location problem | 2 International | 1-median | ORDERED MEDIAN PROBLEMS | Single facility location proble | Exact algorithm | Rectilinear norm | Operations Research/Decision Theory | Convex and Discrete Geometry | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Algorithms | Industrial locations | Demand | Operations research | Production planning | Site selection | Norms | Disks | Combinatorial analysis

Journal Article

Geometry and Topology, ISSN 1364-0380, 2009, Volume 13, Issue 3, pp. 1313 - 1336

Let F = pi(1) (S) where S is a compact, connected, oriented surface with chi(S) < 0 and nonempty boundary. (1) The projective class of the chain partial...

Hyperbolic structure | Polyhedral norm | Rotation number | Bounded cohomology | Immersion | Rigidity | Free group | Scl | Surface | MATHEMATICS | THURSTON NORM | SUBGROUPS | HOMOLOGY

Hyperbolic structure | Polyhedral norm | Rotation number | Bounded cohomology | Immersion | Rigidity | Free group | Scl | Surface | MATHEMATICS | THURSTON NORM | SUBGROUPS | HOMOLOGY

Journal Article

Discrete Optimization, ISSN 1572-5286, 11/2015, Volume 18, pp. 38 - 55

We discuss the computational complexity of special cases of the three-dimensional (axial) assignment problem where the elements are points in a Cartesian space...

Polyhedral norm | 3-dimensional assignment problem | Combinatorial optimization | Computational complexity | 3-dimensional matching problem | TRAVELING SALESMAN PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Computer science

Polyhedral norm | 3-dimensional assignment problem | Combinatorial optimization | Computational complexity | 3-dimensional matching problem | TRAVELING SALESMAN PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Computer science

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 2, pp. 449 - 470

We prove the existence of equivalent polyhedral norms on a number of classes of non-separable spaces, the majority of which being of the form C ( K ) . In...

Polyhedral norm | Tree | Orlicz space | Scattered compact | MATHEMATICS | polyhedral norm | CONVEX-BODIES | APPROXIMATION | scattered compact | tree

Polyhedral norm | Tree | Orlicz space | Scattered compact | MATHEMATICS | polyhedral norm | CONVEX-BODIES | APPROXIMATION | scattered compact | tree

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2008, Volume 46, Issue 3, pp. 1619 - 1639

A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods,...

Finite element method | Approximation | Boundary conditions | Poisson equation | Mathematical functions | Sobolev spaces | Grid refinement | Weighting functions | Triangle inequalities | Singularities | Finite element methods | Least-squares | Weighted Sobolev spaces | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | finite element methods | singularities | PARTIAL-DIFFERENTIAL EQUATIONS | MAXWELL EQUATIONS | FINITE-ELEMENT METHODS | POLYHEDRAL DOMAINS | ASTERISK | least-squares | weighted Sobolev spaces

Finite element method | Approximation | Boundary conditions | Poisson equation | Mathematical functions | Sobolev spaces | Grid refinement | Weighting functions | Triangle inequalities | Singularities | Finite element methods | Least-squares | Weighted Sobolev spaces | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DISCONTINUOUS COEFFICIENTS | finite element methods | singularities | PARTIAL-DIFFERENTIAL EQUATIONS | MAXWELL EQUATIONS | FINITE-ELEMENT METHODS | POLYHEDRAL DOMAINS | ASTERISK | least-squares | weighted Sobolev spaces

Journal Article

Advances in Geometry, ISSN 1615-715X, 07/2007, Volume 7, Issue 3, pp. 391 - 402

We investigate the family M of intersections of balls in a finite-dimensional vector space with a polyhedral norm. The spaces for which M is closed under...

Mazur set | Polyhedral norm | Intersections of balls | Ball stability | Mazur space | MATHEMATICS | polyhedral norm | ball stability | CONVEX-SETS | intersections of balls

Mazur set | Polyhedral norm | Intersections of balls | Ball stability | Mazur space | MATHEMATICS | polyhedral norm | ball stability | CONVEX-SETS | intersections of balls

Journal Article

Optimization Letters, ISSN 1862-4472, 1/2018, Volume 12, Issue 1, pp. 203 - 220

Given the position of some facilities, we study the shape of optimal partitions of the customers’ area in a general planar demand region minimizing total...

Facility location | Computational Intelligence | Polyhedral- and $$\ell _p$$ ℓ p -norms | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Optimal transport | Optimization | Polyhedral- and ℓ | norms | EXISTENCE | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEBER PROBLEM | Polyhedral- and l(p)-norms | DISTANCES | EQUILIBRIUM | NORMS

Facility location | Computational Intelligence | Polyhedral- and $$\ell _p$$ ℓ p -norms | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Optimal transport | Optimization | Polyhedral- and ℓ | norms | EXISTENCE | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEBER PROBLEM | Polyhedral- and l(p)-norms | DISTANCES | EQUILIBRIUM | NORMS

Journal Article

Computers & Industrial Engineering, ISSN 0360-8352, 11/2017, Volume 113, pp. 221 - 240

•Introduces a new problem: Capacitated Multi-facility Weber Problem with polyhedral barriers (CMWP-B).•Two alternate location-allocation type heuristics are...

Polyhedral barriers | Location-allocation | Heuristics | SINGLE | CONVEXITY | ALGORITHMS | KERNEL SEARCH | APPROXIMATE SOLUTION METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORBIDDEN REGIONS | LOCATION-ALLOCATION PROBLEMS | L(P) NORM | CONVERGENCE | ENGINEERING, INDUSTRIAL | TRAVEL DISTANCES

Polyhedral barriers | Location-allocation | Heuristics | SINGLE | CONVEXITY | ALGORITHMS | KERNEL SEARCH | APPROXIMATE SOLUTION METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORBIDDEN REGIONS | LOCATION-ALLOCATION PROBLEMS | L(P) NORM | CONVERGENCE | ENGINEERING, INDUSTRIAL | TRAVEL DISTANCES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2015, Volume 143, Issue 11, pp. 4845 - 4849

We show that if X are Banach spaces, where Y is a bounded linear operator such that T^*(Y^*) of X is separable and isomorphic to a polyhedral space. Some...

Polytopes | Boundaries | Renormings | Polyhedral norms | MATHEMATICS | MATHEMATICS, APPLIED | boundaries | polytopes | renormings

Polytopes | Boundaries | Renormings | Polyhedral norms | MATHEMATICS | MATHEMATICS, APPLIED | boundaries | polytopes | renormings

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2014, Volume 266, Issue 1, pp. 247 - 264

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and...

Polytopes | Polyhedral norms and renormings | Boundaries | Countable covers | MATHEMATICS | ORLICZ SEQUENCE-SPACES | APPROXIMATION | BANACH-SPACES | SMOOTH NORMS | RENORMINGS | C(K) | Mathematics - Functional Analysis

Polytopes | Polyhedral norms and renormings | Boundaries | Countable covers | MATHEMATICS | ORLICZ SEQUENCE-SPACES | APPROXIMATION | BANACH-SPACES | SMOOTH NORMS | RENORMINGS | C(K) | Mathematics - Functional Analysis

Journal Article

SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2017, Volume 55, Issue 4, pp. 2025 - 2049

In this paper we establish a best approximation property of fully discrete Galerkin solutions of second- order parabolic problems on convex polygonal and...

MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | L-INFINITY | parabolic problems | BOUNDARY-CONDITIONS | STABILITY | pointwise control | pointwise error estimates | FINITE-ELEMENT METHODS | EQUATIONS | optimal control | CONVEX POLYHEDRAL DOMAINS | discontinuous Galerkin | CONSTRAINTS | MAXIMUM-NORM | error estimates | QUASI-OPTIMALITY | finite elements | Mathematics - Numerical Analysis

MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | L-INFINITY | parabolic problems | BOUNDARY-CONDITIONS | STABILITY | pointwise control | pointwise error estimates | FINITE-ELEMENT METHODS | EQUATIONS | optimal control | CONVEX POLYHEDRAL DOMAINS | discontinuous Galerkin | CONSTRAINTS | MAXIMUM-NORM | error estimates | QUASI-OPTIMALITY | finite elements | Mathematics - Numerical Analysis

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 12/2014, Volume 68, Issue 12, pp. 2314 - 2330

This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite...

Biharmonic equation | Weak partial derivatives | Weak Galerkin | Finite element methods | Polyhedral meshes | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATIONS | Finite element method | Methods | Biharmonic equations | Mathematical analysis | Norms | Polyhedrons | Mathematical models | Derivatives | Estimates

Biharmonic equation | Weak partial derivatives | Weak Galerkin | Finite element methods | Polyhedral meshes | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATIONS | Finite element method | Methods | Biharmonic equations | Mathematical analysis | Norms | Polyhedrons | Mathematical models | Derivatives | Estimates

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2015, Volume 143, Issue 8, pp. 3413 - 3420

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2014, Volume 30, Issue 3, pp. 1003 - 1029

A new weak Galerkin (WG) finite element method is introduced and analyzed in this article for the biharmonic equation in its primary form. This method is...

biharmonic equations | polyhedral meshes | finite element methods | weak Laplacian | weak Galerkin | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATIONS | Finite element method | Analysis | Methods | Biharmonic equations | Mathematical analysis | Norms | Polyhedrons | Mathematical models | Estimates | Convergence

biharmonic equations | polyhedral meshes | finite element methods | weak Laplacian | weak Galerkin | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | APPROXIMATIONS | Finite element method | Analysis | Methods | Biharmonic equations | Mathematical analysis | Norms | Polyhedrons | Mathematical models | Estimates | Convergence

Journal Article

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