Mathematical Programming, ISSN 0025-5610, 11/2016, Volume 160, Issue 1, pp. 193 - 223

Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators...

Primary 52A41 | 26A51 | 52A30 | 52A25 | Theoretical, Mathematical and Computational Physics | Mathematics | Recession cone | Maximally monotone operator | Nearly equal | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | Numerical Analysis | Relative interior | Subdifferential with nonconvex domain or range | Combinatorics | 47H05 | Secondary 47H04 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FITZPATRICK FUNCTIONS | DUALITY | MONOTONE-OPERATORS | Studies | Mathematical analysis | Convex analysis | Optimization | Differential equations | Functions (mathematics) | Operators (mathematics) | Convexity | Mathematical programming

Primary 52A41 | 26A51 | 52A30 | 52A25 | Theoretical, Mathematical and Computational Physics | Mathematics | Recession cone | Maximally monotone operator | Nearly equal | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | Numerical Analysis | Relative interior | Subdifferential with nonconvex domain or range | Combinatorics | 47H05 | Secondary 47H04 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FITZPATRICK FUNCTIONS | DUALITY | MONOTONE-OPERATORS | Studies | Mathematical analysis | Convex analysis | Optimization | Differential equations | Functions (mathematics) | Operators (mathematics) | Convexity | Mathematical programming

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2005, Volume 127, Issue 1, pp. 45 - 70

In this paper, strong duality for nearly-convex optimization problems is established...

nearly convex functions | Operations Research/Decision Theory | Calculus of Variations and Optimal Control | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Nearly convex sets | strong duality | Optimization | Strong duality | Nearly convex functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | nearly convex sets | Studies | Conjugates

nearly convex functions | Operations Research/Decision Theory | Calculus of Variations and Optimal Control | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Nearly convex sets | strong duality | Optimization | Strong duality | Nearly convex functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | nearly convex sets | Studies | Conjugates

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 03/2019, Volume 180, Issue 3, pp. 751 - 774

The signed distance function (or oriented distance function) of a set in a metric space determines the distance of a given point from the boundary of the set, with the sign determined by whether the point is in the set or in its...

Maximally monotone operator | Skeleton of a convex set | Not convex subdifferential domain | Subdifferential | Paramonotone operator | Signed distance function | Nearly convex sets | Fenchel conjugate | Boundary projection | MATHEMATICS, APPLIED | CONVEXITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | MONOTONE-OPERATORS | Knowledge | Analysis | Domains | Fuzzy sets | Applications of mathematics | Metric space | Mathematical analysis

Maximally monotone operator | Skeleton of a convex set | Not convex subdifferential domain | Subdifferential | Paramonotone operator | Signed distance function | Nearly convex sets | Fenchel conjugate | Boundary projection | MATHEMATICS, APPLIED | CONVEXITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | MONOTONE-OPERATORS | Knowledge | Analysis | Domains | Fuzzy sets | Applications of mathematics | Metric space | Mathematical analysis

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 8/2016, Volume 41, Issue 3, pp. 884 - 897

The problem of finding a minimizer of the sum of two convex functions—or, more generally, that of finding a zero of the sum of two maximally monotone operators...

firmly nonexpansive mapping | displacement mapping | near equality | subdifferential operator | convex function | nearly convex set | range | normal problem | Douglas–Rachford splitting operator | Brezis–Haraux theorem | maximally monotone operator | Attouch–Théra duality | Brezis-Haraux theorem | Maximally monotone operator | Near equality | Normal problem | Douglas-Rachford splitting operator | Nearly convex set | Firmly nonexpansive mapping | Subdifferential operator | Attouch-thera duality | Displacement mapping | Convex function | Range | MATHEMATICS, APPLIED | Attouch-Thera duality | SUM | PARAMONOTONICITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DUALITY | MONOTONE-OPERATORS | Transformations (Mathematics) | Analysis | Convex functions

firmly nonexpansive mapping | displacement mapping | near equality | subdifferential operator | convex function | nearly convex set | range | normal problem | Douglas–Rachford splitting operator | Brezis–Haraux theorem | maximally monotone operator | Attouch–Théra duality | Brezis-Haraux theorem | Maximally monotone operator | Near equality | Normal problem | Douglas-Rachford splitting operator | Nearly convex set | Firmly nonexpansive mapping | Subdifferential operator | Attouch-thera duality | Displacement mapping | Convex function | Range | MATHEMATICS, APPLIED | Attouch-Thera duality | SUM | PARAMONOTONICITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DUALITY | MONOTONE-OPERATORS | Transformations (Mathematics) | Analysis | Convex functions

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2019, Volume 480, Issue 1, p. 123368

Let F be a Banach space of continuous functions over a connected locally compact space X. We present several sufficient conditions on F guaranteeing that the...

Multiplication operators | Surjective isometries | Function spaces | Birkhoff orthogonality | Nearly strictly convex spaces | SPACE | MATHEMATICS | WEIGHTED COMPOSITION OPERATORS | MATHEMATICS, APPLIED | Surjective isometrics | UNITARY | Mathematics - Functional Analysis

Multiplication operators | Surjective isometries | Function spaces | Birkhoff orthogonality | Nearly strictly convex spaces | SPACE | MATHEMATICS | WEIGHTED COMPOSITION OPERATORS | MATHEMATICS, APPLIED | Surjective isometrics | UNITARY | Mathematics - Functional Analysis

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 95 - 102

... (resp. weakly) open set $$W\supset P_A(x)$$ W ⊃ P A ( x ) , any $$\{x_n\}_{n=1}^{\infty }\subset X$$ { x n } n = 1 ∞ ⊂ X with $$x_n\rightarrow x$$ x n → x and any sequence...

Metric projection | Primary 41A65 | Secondary 46B20 | Property S (WS) | Theoretical, Mathematical and Computational Physics | Proximinal set | Nearly strongly (very) convex space | Mathematics, general | Mathematics | Continuity | Applications of Mathematics | Hausdorff (Wijsman) convergence | MATHEMATICS | APPROXIMATIONS | CONVEXITY | CONVERGENCE | Projection | Mapping | Banach space

Metric projection | Primary 41A65 | Secondary 46B20 | Property S (WS) | Theoretical, Mathematical and Computational Physics | Proximinal set | Nearly strongly (very) convex space | Mathematics, general | Mathematics | Continuity | Applications of Mathematics | Hausdorff (Wijsman) convergence | MATHEMATICS | APPROXIMATIONS | CONVEXITY | CONVERGENCE | Projection | Mapping | Banach space

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 9, pp. 1622 - 1624

Properties for convex cones are discussed, and are used to obtain the following results...

Ic-cone-convexness | Nearly cone-subconvexlikeness | Convex cone | MATHEMATICS, APPLIED | SET-VALUED MAPS | VECTOR OPTIMIZATION | Cones | Equivalence | Order disorder | Mathematical analysis

Ic-cone-convexness | Nearly cone-subconvexlikeness | Convex cone | MATHEMATICS, APPLIED | SET-VALUED MAPS | VECTOR OPTIMIZATION | Cones | Equivalence | Order disorder | Mathematical analysis

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2013, Volume 139, Issue 1, pp. 55 - 70

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings...

52A20 | Theoretical, Mathematical and Computational Physics | Asymptotic regularity | Mathematics | Monotone operator | Mathematical Methods in Physics | 47H10 | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | 47H09 | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | PROXIMAL AVERAGE | DUALITY | Studies | Mapping | Asymptotic methods | Analysis | Mathematical programming | Operators | Convexity | Asymptotic properties | Sums

52A20 | Theoretical, Mathematical and Computational Physics | Asymptotic regularity | Mathematics | Monotone operator | Mathematical Methods in Physics | 47H10 | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | 47H09 | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | PROXIMAL AVERAGE | DUALITY | Studies | Mapping | Asymptotic methods | Analysis | Mathematical programming | Operators | Convexity | Asymptotic properties | Sums

Journal Article

Optimization Letters, ISSN 1862-4472, 1/2014, Volume 8, Issue 1, pp. 237 - 246

We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex...

Fitzpatrick function | Set-valued operator | 47B65 | Mathematics | Monotone operator | Optimization | Maximally monotone operator | Computational Intelligence | Secondary 26B25 | Primary 47H05 | Nearly convex set | 47A05 | Operations Research/Decision Theory | Numerical and Computational Physics | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIFUNCTIONS | SUM

Fitzpatrick function | Set-valued operator | 47B65 | Mathematics | Monotone operator | Optimization | Maximally monotone operator | Computational Intelligence | Secondary 26B25 | Primary 47H05 | Nearly convex set | 47A05 | Operations Research/Decision Theory | Numerical and Computational Physics | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIFUNCTIONS | SUM

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 2005, Volume 62, Issue 2, pp. 187 - 209

In this paper we consider vector optimization problems where objective and constraints are set-valued maps...

Optimality conditions | ε-weak Pareto | Convex | Multiobjective optimization | Scalarization | ε-subdifferentials of set-valued maps | Nearly subconvexlike | Subconvexlike | Lagrange-multipliers | MATHEMATICS, APPLIED | epsilon-subdifferentials of set-valued maps | scalarization | nearly subconvexlike | MAXIMIZATIONS | subconvexlike | CONVEX VECTOR OPTIMIZATION | optimality conditions | multiobjective optimization | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | epsilon-weak Pareto | convex | EFFICIENCY

Optimality conditions | ε-weak Pareto | Convex | Multiobjective optimization | Scalarization | ε-subdifferentials of set-valued maps | Nearly subconvexlike | Subconvexlike | Lagrange-multipliers | MATHEMATICS, APPLIED | epsilon-subdifferentials of set-valued maps | scalarization | nearly subconvexlike | MAXIMIZATIONS | subconvexlike | CONVEX VECTOR OPTIMIZATION | optimality conditions | multiobjective optimization | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | epsilon-weak Pareto | convex | EFFICIENCY

Journal Article

Journal of Geometry, ISSN 0047-2468, 8/2018, Volume 109, Issue 2, pp. 1 - 9

.../10.1007/s00022-018-0433-3 Journal of Geometry Putting convex d -polytopes inside frames Joseph Zaks Abstract. We introduce a construction of large neighborly...

Geometry | 52B10 | 52B11 | Mathematics | Nearly-neighborly families | Neighborly families | Rods and frames | Family

Geometry | 52B10 | 52B11 | Mathematics | Nearly-neighborly families | Neighborly families | Rods and frames | Family

Journal Article

Annals of Functional Analysis, ISSN 2008-8752, 2017, Volume 8, Issue 1, pp. 16 - 26

... of the unit ball of the bidual space. For any closed convex set C C X and x is an element of X \ C with Pc(x...

Nearly very convex point | Nearly rotund point | Approximatively weak compactness | S point | Nested sequence of balls | nearly very convex point | MATHEMATICS | nested sequence of balls | MATHEMATICS, APPLIED | approximatively weak compactness | nearly rotund point | BANACH-SPACES

Nearly very convex point | Nearly rotund point | Approximatively weak compactness | S point | Nested sequence of balls | nearly very convex point | MATHEMATICS | nested sequence of balls | MATHEMATICS, APPLIED | approximatively weak compactness | nearly rotund point | BANACH-SPACES

Journal Article

IET Radar, Sonar & Navigation, ISSN 1751-8784, 2/2018, Volume 12, Issue 2, pp. 227 - 238

... (OPCWEM) and its mismatched filters design. Specifically, they first propose a minimisation criterion to design nearly OPCWEM, which is a non-convex optimisation problem and solved by a least-pth minimax algorithm...

Research Article | SEQUENCE SETS | radar antennas | ANTENNAS | minimax techniques | radar signal processing | nonconvex optimisation problem | MIMO radar | minimisation criterion to | antenna arrays | sidelobe level suppression | TARGET DETECTION | phase-coded waveforms-with-expanded mainlobes | mismatched filter design | concave programming | min-max criterion | convex optimisation problem | Doppler sensitivity | filtering theory | expanded mainlobe | nearly orthogonal waveforms | OPCWEM | convex programming | TELECOMMUNICATIONS | least-pth minimax algorithm | ENGINEERING, ELECTRICAL & ELECTRONIC | distributed multiple-input-multiple-output radar waveform | constant-modulus requirement | ORTHOGONAL NETTED RADAR | SYSTEMS | minimisation

Research Article | SEQUENCE SETS | radar antennas | ANTENNAS | minimax techniques | radar signal processing | nonconvex optimisation problem | MIMO radar | minimisation criterion to | antenna arrays | sidelobe level suppression | TARGET DETECTION | phase-coded waveforms-with-expanded mainlobes | mismatched filter design | concave programming | min-max criterion | convex optimisation problem | Doppler sensitivity | filtering theory | expanded mainlobe | nearly orthogonal waveforms | OPCWEM | convex programming | TELECOMMUNICATIONS | least-pth minimax algorithm | ENGINEERING, ELECTRICAL & ELECTRONIC | distributed multiple-input-multiple-output radar waveform | constant-modulus requirement | ORTHOGONAL NETTED RADAR | SYSTEMS | minimisation

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 9/2015, Volume 109, Issue 2, pp. 407 - 416

... · Pre-duality mapping · α -upper semi-continuity · Usco mapping · Nearly strongly convex space · Nearly uniformly convex space · Nearly very convex space...

Usco mapping | Theoretical, Mathematical and Computational Physics | Mathematics | Nearly strongly convex space | Nearly uniformly convex space | Pre-duality mapping | Nearly very convex space | alpha $$ α -upper semi-continuity | Secondary 46E30 | Primary 46B20 | Mathematics, general | Applications of Mathematics | Duality mapping | α-upper semi-continuity | MATHEMATICS | alpha-upper semi-continuity | DROP PROPERTY

Usco mapping | Theoretical, Mathematical and Computational Physics | Mathematics | Nearly strongly convex space | Nearly uniformly convex space | Pre-duality mapping | Nearly very convex space | alpha $$ α -upper semi-continuity | Secondary 46E30 | Primary 46B20 | Mathematics, general | Applications of Mathematics | Duality mapping | α-upper semi-continuity | MATHEMATICS | alpha-upper semi-continuity | DROP PROPERTY

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2010, Volume 30, Issue 4, pp. 1154 - 1166

... （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency...

标量化定理 | 拉格朗日乘数 | 可分条件 | 可行集 | 凸集值映射 | Benson真有效性 | 向量优化问题 | nearly cone-subconvexlike set-valued map | scalarization | 90C29 | Benson proper efficiency | Locally convex space | 46A03 | Scalarization | Nearly cone-subconvexlike set-valued map | MATHEMATICS | VECTOR OPTIMIZATION | MAPS | SET-VALUED FUNCTIONS

标量化定理 | 拉格朗日乘数 | 可分条件 | 可行集 | 凸集值映射 | Benson真有效性 | 向量优化问题 | nearly cone-subconvexlike set-valued map | scalarization | 90C29 | Benson proper efficiency | Locally convex space | 46A03 | Scalarization | Nearly cone-subconvexlike set-valued map | MATHEMATICS | VECTOR OPTIMIZATION | MAPS | SET-VALUED FUNCTIONS

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2019, Volume 200, Issue 1, pp. 351 - 362

The homogeneous nearly Kähler structure on $$S^3\times S^3$$ S 3 × S 3 is the only known complete 6-dimensional strictly nearly Kähler structure which is...

53C30 | Torus actions | Moment maps | 53D20 | Mathematics | Topology | 53C25 | Homogeneous spaces | Convex and Discrete Geometry | Algebraic Geometry | Nearly Kähler | Hyperbolic Geometry | Projective Geometry | Differential Geometry

53C30 | Torus actions | Moment maps | 53D20 | Mathematics | Topology | 53C25 | Homogeneous spaces | Convex and Discrete Geometry | Algebraic Geometry | Nearly Kähler | Hyperbolic Geometry | Projective Geometry | Differential Geometry

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2019, Volume 50, Issue 4, pp. 363 - 378

We introduce a new class of line arrangements in the projective plane, called nearly supersolvable, and show that any arrangement in this class is either free...

Terao’s conjecture | Tjurina number | Slope Problem | Mathematics | Jacobian syzygy | Free line arrangement | Primary 14H50 | 13D02 | Secondary 14B05 | 32S22 | Nearly free line arrangement | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Algebraic Geometry

Terao’s conjecture | Tjurina number | Slope Problem | Mathematics | Jacobian syzygy | Free line arrangement | Primary 14H50 | 13D02 | Secondary 14B05 | 32S22 | Nearly free line arrangement | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Algebraic Geometry

Journal Article

ACTA MATHEMATICA SCIENTIA, ISSN 0252-9602, 01/2005, Volume 25, Issue 1, pp. 152 - 160

Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions...

MATHEMATICS | MAPS | Lagrangian multipliers | scalarization | super efficiency | OPTIMALITY CONDITIONS | nearly cone-subconvexlikeness | convex cones

MATHEMATICS | MAPS | Lagrangian multipliers | scalarization | super efficiency | OPTIMALITY CONDITIONS | nearly cone-subconvexlikeness | convex cones

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 3/2007, Volume 132, Issue 3, pp. 509 - 515

.... These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions...

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Nearly convex functions | Fenchel duality | Conjugate functions | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | nearly convex functions | conjugate functions | Studies | Theorems | Hypotheses | Duality theorem | Convexity

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Nearly convex functions | Fenchel duality | Conjugate functions | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | nearly convex functions | conjugate functions | Studies | Theorems | Hypotheses | Duality theorem | Convexity

Journal Article

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Full Text
SOLVING LP RELAXATIONS OF SOME NP-HARD PROBLEMS IS AS HARD AS SOLVING ANY LINEAR PROGRAM

SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2019, Volume 29, Issue 3, pp. 1745 - 1771

.... We distinguish two types of such reductions. In the first type (shown for set cover/packing, facility location, maximum satisfiability, maximum independent set, and multiway cut...

universality | combinatorial optimization | MATHEMATICS, APPLIED | linear programming relaxation | log-space reduction | extension complexity | ALGORITHMS | nearly linear-time reduction | convex polytope | LP-completeness

universality | combinatorial optimization | MATHEMATICS, APPLIED | linear programming relaxation | log-space reduction | extension complexity | ALGORITHMS | nearly linear-time reduction | convex polytope | LP-completeness

Journal Article

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