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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
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
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
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
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
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
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
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
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
Journal Article
Optimization Letters, ISSN 1862-4472, 1/2018, Volume 12, Issue 1, pp. 203 - 220
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
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
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
Journal Article
SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2017, Volume 55, Issue 4, pp. 2025 - 2049
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
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
Journal Article
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