Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2016, Volume 171, Issue 3, pp. 865 - 886

The paper addresses the problem of recovering a pseudoconvex function from the normal cones to its level sets that we call the convex level sets integration problem...

Revealed preferences | Monotonicity and pseudomonotonicity | Mathematics | Theory of Computation | Optimization | Maximality | 91B42 | Calculus of Variations and Optimal Control; Optimization | 91B16 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 26B25 | Convexity and pseudoconvexity | CRITERIA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPS | REVEALED PREFERENCE | Business schools | Differential equations | Studies | Ordinary differential equations | Mathematical models | Convex analysis | Euclidean geometry | Cones | Mathematical analysis | Uniqueness | Boundaries | Bundles

Revealed preferences | Monotonicity and pseudomonotonicity | Mathematics | Theory of Computation | Optimization | Maximality | 91B42 | Calculus of Variations and Optimal Control; Optimization | 91B16 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 26B25 | Convexity and pseudoconvexity | CRITERIA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPS | REVEALED PREFERENCE | Business schools | Differential equations | Studies | Ordinary differential equations | Mathematical models | Convex analysis | Euclidean geometry | Cones | Mathematical analysis | Uniqueness | Boundaries | Bundles

Journal Article

IEEE transactions on smart grid, ISSN 1949-3061, 2015, Volume 6, Issue 1, pp. 124 - 134

Microgrid is a key enabling solution to future smart grids by integrating distributed renewable generators and storage systems to efficiently serve the local...

smart grid | distributed storage | online algorithm | Microgrids | Optimization | Renewable energy sources | renewable energy | Convex optimization | microgrid | Prediction algorithms | energy management | Real-time systems | Energy storage | Load modeling | SYSTEM | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Dynamic programming | Energy management | Renewable resources

smart grid | distributed storage | online algorithm | Microgrids | Optimization | Renewable energy sources | renewable energy | Convex optimization | microgrid | Prediction algorithms | energy management | Real-time systems | Energy storage | Load modeling | SYSTEM | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Dynamic programming | Energy management | Renewable resources

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 2018, Volume 50, Issue 4, pp. 3791 - 3841

In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences...

Higher Sobolev regularity | Elasticity | Martensitic phase transitions | Convex integration | Weak isometric immersions | Differential inclusion | RIGIDITY RESULT | MATHEMATICS, APPLIED | LINEAR-THEORY | elasticity | higher Sobolev regularity | MICROSTRUCTURES | weak isometric immersions | SURFACE-ENERGY | differential inclusion | convex integration | martensitic phase transitions | PHASE-TRANSITION | ISOMETRIC MAPS

Higher Sobolev regularity | Elasticity | Martensitic phase transitions | Convex integration | Weak isometric immersions | Differential inclusion | RIGIDITY RESULT | MATHEMATICS, APPLIED | LINEAR-THEORY | elasticity | higher Sobolev regularity | MICROSTRUCTURES | weak isometric immersions | SURFACE-ENERGY | differential inclusion | convex integration | martensitic phase transitions | PHASE-TRANSITION | ISOMETRIC MAPS

Journal Article

Journal of Complexity, ISSN 0885-064X, 02/2019, Volume 50, pp. 25 - 42

We prove the curse of dimensionality in the worst case setting for multivariate numerical integration for various classes of smooth functions...

Tractability | [formula omitted]-condition | Thin-shell estimate | Numerical integration | Curse of dimension | Isotropic convex body | condition | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX | SURFACE MEASURE | SPHERE | BODIES | Psi-condition

Tractability | [formula omitted]-condition | Thin-shell estimate | Numerical integration | Curse of dimension | Isotropic convex body | condition | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX | SURFACE MEASURE | SPHERE | BODIES | Psi-condition

Journal Article

Computational Mechanics, ISSN 0178-7675, 12/2015, Volume 56, Issue 6, pp. 967 - 981

We present a method for the numerical integration of homogeneous functions over convex and nonconvex polygons and polyhedra. On applying...

Engineering | Numerical integration | Weakly singular integrals | Euler’s homogeneous function theorem | Cubature rule | Stokes’s theorem | Convex and nonconvex polytopes | Theoretical and Applied Mechanics | Computational Science and Engineering | Classical Continuum Physics | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Euler's homogeneous function theorem | Cubature rule Stokes's theorem | FINITE-ELEMENT-METHOD | Polytopes | Polyhedra | Mathematical analysis | Polyhedrons | Mathematical models | Polynomials | Polygons | Numerical Analysis | Mathematics | Computer Science

Engineering | Numerical integration | Weakly singular integrals | Euler’s homogeneous function theorem | Cubature rule | Stokes’s theorem | Convex and nonconvex polytopes | Theoretical and Applied Mechanics | Computational Science and Engineering | Classical Continuum Physics | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Euler's homogeneous function theorem | Cubature rule Stokes's theorem | FINITE-ELEMENT-METHOD | Polytopes | Polyhedra | Mathematical analysis | Polyhedrons | Mathematical models | Polynomials | Polygons | Numerical Analysis | Mathematics | Computer Science

Journal Article

Analysis and PDE, ISSN 2157-5045, 2017, Volume 10, Issue 3, pp. 695 - 727

.... In particular, we focus on degenerate, i.e., "flexible", weak solutions that can be constructed through methods of convex integration a la Nash and Kuiper and establish...

Convex integration | Rigidity and flexibility | Developable surfaces | H-principle | Monge-Ampére equation | DISSIPATION | MATHEMATICS, APPLIED | CODIMENSION | Monge-Ampere equation | developable surfaces | PERONA-MALIK EQUATION | ISOMETRIC IMMERSIONS | DIFFERENTIAL INCLUSION | GRADIENT RANGE | MATHEMATICS | convex integration | REGULARITY | h-principle | MAPPINGS | WEAK SOLUTIONS | EULER EQUATIONS | rigidity and flexibility

Convex integration | Rigidity and flexibility | Developable surfaces | H-principle | Monge-Ampére equation | DISSIPATION | MATHEMATICS, APPLIED | CODIMENSION | Monge-Ampere equation | developable surfaces | PERONA-MALIK EQUATION | ISOMETRIC IMMERSIONS | DIFFERENTIAL INCLUSION | GRADIENT RANGE | MATHEMATICS | convex integration | REGULARITY | h-principle | MAPPINGS | WEAK SOLUTIONS | EULER EQUATIONS | rigidity and flexibility

Journal Article

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 5/2012, Volume 109, Issue 19, pp. 7218 - 7223

.... Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems...

Squares | Maps | Integration theorems | Vector fields | Sine function | Fractals | Matrices | Mathematical inequalities | Curvature | Curves | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Algorithms | Image Processing, Computer-Assisted - methods | Imaging, Three-Dimensional | Physics - methods | Usage | Convex functions | Research | Riemann integral | Differential Geometry | Mathematics | Physical Sciences

Squares | Maps | Integration theorems | Vector fields | Sine function | Fractals | Matrices | Mathematical inequalities | Curvature | Curves | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Algorithms | Image Processing, Computer-Assisted - methods | Imaging, Three-Dimensional | Physics - methods | Usage | Convex functions | Research | Riemann integral | Differential Geometry | Mathematics | Physical Sciences

Journal Article

Complex analysis and operator theory, ISSN 1661-8262, 2018, Volume 13, Issue 4, pp. 1883 - 1893

We study the integration operator between the growth spaces $$H_w^\infty $$ H w ∞ and $$H_u^\infty $$ H u ∞ on the complex plane with arbitrary radial weights w and u...

Operator Theory | Differentiation operator | 47B38 | Growth space | Analysis | Mathematics, general | Mathematics | Associated weight | Primary 30D15 | Secondary 26A51 | 30H99 | Log-convex weight

Operator Theory | Differentiation operator | 47B38 | Growth space | Analysis | Mathematics, general | Mathematics | Associated weight | Primary 30D15 | Secondary 26A51 | 30H99 | Log-convex weight

Journal Article

Abstract and applied analysis, ISSN 1687-0409, 2012, Volume 2012, pp. 1 - 10

We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral...

MATHEMATICS, APPLIED | Studies | Mathematics | Convex analysis | Inequality

MATHEMATICS, APPLIED | Studies | Mathematics | Convex analysis | Inequality

Journal Article

The Journal of geometric analysis, ISSN 1559-002X, 2018, Volume 29, Issue 1, pp. 328 - 369

We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets...

Abstract Harmonic Analysis | 65D30 | Fourier Analysis | Discrepancy | Numerical integration | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 11K38 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Metric measure spaces | MATHEMATICS | SOBOLEV SPACES | INEQUALITIES | CUBATURE ERROR | BOUNDS | SPHERE | QUADRATURE

Abstract Harmonic Analysis | 65D30 | Fourier Analysis | Discrepancy | Numerical integration | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 11K38 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Metric measure spaces | MATHEMATICS | SOBOLEV SPACES | INEQUALITIES | CUBATURE ERROR | BOUNDS | SPHERE | QUADRATURE

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1188 - 1201

Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions...

Epi-pointed functions | Conjugate function | Integration | [formula omitted]-subdifferential | Lower semicontinuous convex envelope | ε-subdifferential | epsilon-subdifferential | CRITERIA | MATHEMATICS, APPLIED | DIFFERENTIABILITY | CALCULUS | PROPERTY | REPRESENTATION | MONOTONICITY | CONVEX-FUNCTIONS | MATHEMATICS | Conjugates | Envelopes | Nonlinearity | Construction | Banach space

Epi-pointed functions | Conjugate function | Integration | [formula omitted]-subdifferential | Lower semicontinuous convex envelope | ε-subdifferential | epsilon-subdifferential | CRITERIA | MATHEMATICS, APPLIED | DIFFERENTIABILITY | CALCULUS | PROPERTY | REPRESENTATION | MONOTONICITY | CONVEX-FUNCTIONS | MATHEMATICS | Conjugates | Envelopes | Nonlinearity | Construction | Banach space

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 4, pp. 2770 - 2794

.... We finally fulfill this density hypothesis by convex integration based on certain approximations from an explicit formula of lamination convex hull of some matrix set involved.

Convex integration | Infinitely many weak solutions on convex domains | Perona-Malik equation | Differential inclusion | Baire's category method | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | differential inclusion | convex integration | infinitely many weak solutions on convex domains | DIFFUSION-EQUATIONS

Convex integration | Infinitely many weak solutions on convex domains | Perona-Malik equation | Differential inclusion | Baire's category method | EXISTENCE | MATHEMATICS, APPLIED | ENERGY | differential inclusion | convex integration | infinitely many weak solutions on convex domains | DIFFUSION-EQUATIONS

Journal Article

SIAM review, ISSN 1095-7200, 2009, Volume 51, Issue 4, pp. 722 - 743

... of the integral on K of any given polynomial; the extension to integration against some weight functions is also provided...

Polytopes | PROBLEMS and TECHNIQUES | Approximation | Optimal solutions | Lebesgue measures | Polynomials | Mathematical moments | Indicator functions | Borel measures | Degrees of polynomials | Computational geometry | Integration | Semidefinite programming | K-moment problem | Volume | MATHEMATICS, APPLIED | CONVEX POLYHEDRA | ALGORITHM | computational geometry | volume | semidefinite programming | POLYNOMIALS | SEMI-ALGEBRAIC SETS | VS. LP RELAXATIONS | POLYTOPE | COMPLEXITY | integration | OPTIMIZATION | POINTS | MOMENTS | Approximation theory | Numerical integration | K-theory | Analysis | Methods

Polytopes | PROBLEMS and TECHNIQUES | Approximation | Optimal solutions | Lebesgue measures | Polynomials | Mathematical moments | Indicator functions | Borel measures | Degrees of polynomials | Computational geometry | Integration | Semidefinite programming | K-moment problem | Volume | MATHEMATICS, APPLIED | CONVEX POLYHEDRA | ALGORITHM | computational geometry | volume | semidefinite programming | POLYNOMIALS | SEMI-ALGEBRAIC SETS | VS. LP RELAXATIONS | POLYTOPE | COMPLEXITY | integration | OPTIMIZATION | POINTS | MOMENTS | Approximation theory | Numerical integration | K-theory | Analysis | Methods

Journal Article

Journal of scientific computing, ISSN 1573-7691, 2018, Volume 77, Issue 3, pp. 1339 - 1370

In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral...

65D30 | Computational Mathematics and Numerical Analysis | Polygonal/polyhedral meshes | Algorithms | Numerical integration | hp -discontinuous Galerkin method | 65L60 | Theoretical, Mathematical and Computational Physics | 65D32 | Mathematical and Computational Engineering | Mathematics | hp-discontinuous Galerkin method | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONERS | GAUSSIAN QUADRATURE-RULES | 2ND-ORDER ELLIPTIC PROBLEMS | DISCRETIZATIONS | ORDER | CONVEX | DIFFERENCE METHOD | DIFFUSION-PROBLEMS | CONVERGENCE | POLYGONS | Finite element method | Methods | Differential equations

65D30 | Computational Mathematics and Numerical Analysis | Polygonal/polyhedral meshes | Algorithms | Numerical integration | hp -discontinuous Galerkin method | 65L60 | Theoretical, Mathematical and Computational Physics | 65D32 | Mathematical and Computational Engineering | Mathematics | hp-discontinuous Galerkin method | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONERS | GAUSSIAN QUADRATURE-RULES | 2ND-ORDER ELLIPTIC PROBLEMS | DISCRETIZATIONS | ORDER | CONVEX | DIFFERENCE METHOD | DIFFUSION-PROBLEMS | CONVERGENCE | POLYGONS | Finite element method | Methods | Differential equations

Journal Article

Computers & chemical engineering, ISSN 0098-1354, 2011, Volume 35, Issue 8, pp. 1558 - 1574

► Eco-industrial parks share wastewater treatment units from several plants. ► A superstructure for water integration in eco-industrial parks is formulated...

Convex discretization | Eco-industrial parks | Recycle/reuse networks | Water integration | Optimization | Inter-plant water integration | DESIGN | RECYCLE | WASTE-INTERCEPTION | REGENERATION | AUTOMATED TARGETING TECHNIQUE | CASCADE ANALYSIS | NETWORKS | MATERIAL REUSE | RESOURCE CONSERVATION | ENGINEERING, CHEMICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Environmental aspects | Algorithms | Pollutants | Parks | Mathematical optimization | Analysis | Networks | Policies | Mathematical models | Cost engineering | Waste water

Convex discretization | Eco-industrial parks | Recycle/reuse networks | Water integration | Optimization | Inter-plant water integration | DESIGN | RECYCLE | WASTE-INTERCEPTION | REGENERATION | AUTOMATED TARGETING TECHNIQUE | CASCADE ANALYSIS | NETWORKS | MATERIAL REUSE | RESOURCE CONSERVATION | ENGINEERING, CHEMICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Environmental aspects | Algorithms | Pollutants | Parks | Mathematical optimization | Analysis | Networks | Policies | Mathematical models | Cost engineering | Waste water

Journal Article

Journal of Engineering Mechanics, ISSN 0733-9399, 05/2016, Volume 142, Issue 5, p. 4016022

AbstractIn structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion...

Technical Papers | Structural dynamics | Accuracy | Nonlinear | Convex optimization | Lyapunov stability | Explicit | Direct integration algorithm | Implicit | Mechanics | Usage | Research | Convex programming

Technical Papers | Structural dynamics | Accuracy | Nonlinear | Convex optimization | Lyapunov stability | Explicit | Direct integration algorithm | Implicit | Mechanics | Usage | Research | Convex programming

Journal Article

Journal of elasticity, ISSN 1573-2681, 2019, Volume 138, Issue 1, pp. 1 - 76

In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials...

Higher Sobolev regularity | Elasticity | Convex integration solutions | Differential inclusion | Solid-solid phase transformations | RIGIDITY RESULT | MATERIALS SCIENCE, MULTIDISCIPLINARY | ELECTRON-DIFFRACTION | MICROSCOPY | MINIMIZERS | MICROSTRUCTURES | MECHANICS | SURFACE-ENERGY | ENGINEERING, MULTIDISCIPLINARY | LEAD ORTHO-VANADATE | TRANSITIONS

Higher Sobolev regularity | Elasticity | Convex integration solutions | Differential inclusion | Solid-solid phase transformations | RIGIDITY RESULT | MATERIALS SCIENCE, MULTIDISCIPLINARY | ELECTRON-DIFFRACTION | MICROSCOPY | MINIMIZERS | MICROSTRUCTURES | MECHANICS | SURFACE-ENERGY | ENGINEERING, MULTIDISCIPLINARY | LEAD ORTHO-VANADATE | TRANSITIONS

Journal Article

IEEE transactions on industrial electronics (1982), ISSN 1557-9948, 2015, Volume 62, Issue 12, pp. 7847 - 7858

System integration and power-flow control of on-board power sources are critical to the performance and cost competitiveness of hybrid electric vehicles (HEVs...

Component Sizing | Torque | Multi-criteria Optimization | Hydrogen | Fuel cells | Hybrid Vehicle | Integrated circuit modeling | Energy management | Optimization | Vehicles | BATTERY | SYSTEM | DESIGN | MODEL | hybrid vehicle | Component sizing | ENGINEERING, ELECTRICAL & ELECTRONIC | STACK | MACHINES | INSTRUMENTS & INSTRUMENTATION | fuel cell | multicriteria optimization | convex optimization | energy management | FUEL-CELL HYBRID | AUTOMATION & CONTROL SYSTEMS | Multiple criteria decision making | Pareto optimum | ENERGY MANAGEMENT | Vehicle Engineering | CONVEX-OPTIMIZATION | LIFETIME | multicriteria | PARTICLE SWARM OPTIMIZATION | Farkostteknik

Component Sizing | Torque | Multi-criteria Optimization | Hydrogen | Fuel cells | Hybrid Vehicle | Integrated circuit modeling | Energy management | Optimization | Vehicles | BATTERY | SYSTEM | DESIGN | MODEL | hybrid vehicle | Component sizing | ENGINEERING, ELECTRICAL & ELECTRONIC | STACK | MACHINES | INSTRUMENTS & INSTRUMENTATION | fuel cell | multicriteria optimization | convex optimization | energy management | FUEL-CELL HYBRID | AUTOMATION & CONTROL SYSTEMS | Multiple criteria decision making | Pareto optimum | ENERGY MANAGEMENT | Vehicle Engineering | CONVEX-OPTIMIZATION | LIFETIME | multicriteria | PARTICLE SWARM OPTIMIZATION | Farkostteknik

Journal Article

Computational geometry : theory and applications, ISSN 0925-7721, 2013, Volume 46, Issue 3, pp. 232 - 252

We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed-ups and extensions of...

Polyhedral computation | Volume computation | Exact integration | Integration of polynomials | Valuations | RATIONAL GENERATING-FUNCTIONS | MATHEMATICS, APPLIED | CONVEX POLYHEDRON | ALGORITHM | MATHEMATICS | POLYTOPE VOLUME COMPUTATION | COMPLEXITY | FRAMEWORK | Computer software industry | Software | Algorithms | Polyhedra | Computation | Integrals | Polyhedrons | Combinatorial analysis | Computer programs

Polyhedral computation | Volume computation | Exact integration | Integration of polynomials | Valuations | RATIONAL GENERATING-FUNCTIONS | MATHEMATICS, APPLIED | CONVEX POLYHEDRON | ALGORITHM | MATHEMATICS | POLYTOPE VOLUME COMPUTATION | COMPLEXITY | FRAMEWORK | Computer software industry | Software | Algorithms | Polyhedra | Computation | Integrals | Polyhedrons | Combinatorial analysis | Computer programs

Journal Article