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

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 | Eulerâ€™s homogeneous function theorem | Cubature rule | Stokesâ€™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 | Eulerâ€™s homogeneous function theorem | Cubature rule | Stokesâ€™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

Proceedings of the National Academy of Sciences - PNAS, 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 âˆž and $$H_u^\infty $$ H u âˆž 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

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

â–º Eco-industrial parks share wastewater treatment units from several plants. â–º 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

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

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

Journal of Engineering Mechanics, ISSN 0733-9399, 12/2016, Volume 142, Issue 12, p. 4016098

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

Technical Papers | Structural dynamics | Nonlinear | Strictly positive realness | Convex optimization | Multi-degree-of-freedom (MDOF) | Lyapunov stability | Explicit | Direct integration algorithm | TIME | POSITIVE REAL LEMMA | ENGINEERING, MECHANICAL | Nonlinear dynamics | Shear | Algorithms | Differential equations | Nonlinearity | Stability analysis | Softening | Dynamical systems

Technical Papers | Structural dynamics | Nonlinear | Strictly positive realness | Convex optimization | Multi-degree-of-freedom (MDOF) | Lyapunov stability | Explicit | Direct integration algorithm | TIME | POSITIVE REAL LEMMA | ENGINEERING, MECHANICAL | Nonlinear dynamics | Shear | Algorithms | Differential equations | Nonlinearity | Stability analysis | Softening | Dynamical systems

Journal Article

EURASIP Journal on Wireless Communications and Networking, ISSN 1687-1472, 12/2017, Volume 2017, Issue 1, pp. 1 - 16

...) problem in the context of physical-layer service integration. Since this biobjective...

Information Systems Applications (incl.Internet) | Secrecy rate region | Engineering | Physical-layer service integration | Signal,Image and Speech Processing | Convex optimization | Communications Engineering, Networks | Artificial noise | COMMON | SECRECY RATE OPTIMIZATIONS | PHYSICAL LAYER SECURITY | WIRELESS NETWORKS | TELECOMMUNICATIONS | CAPACITY REGION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical optimization | Analysis | MIMO communications | Multicast | MIMO (control systems) | Maximization | Messages | Computer simulation | Pareto optimum | Noise | Receivers | Broadcasting | Optimization | Complexity

Information Systems Applications (incl.Internet) | Secrecy rate region | Engineering | Physical-layer service integration | Signal,Image and Speech Processing | Convex optimization | Communications Engineering, Networks | Artificial noise | COMMON | SECRECY RATE OPTIMIZATIONS | PHYSICAL LAYER SECURITY | WIRELESS NETWORKS | TELECOMMUNICATIONS | CAPACITY REGION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical optimization | Analysis | MIMO communications | Multicast | MIMO (control systems) | Maximization | Messages | Computer simulation | Pareto optimum | Noise | Receivers | Broadcasting | Optimization | Complexity

Journal Article

16.
Full Text
Stochastic integration and stochastic PDEs driven by jumps on the dual of a nuclear space

Stochastic partial differential equations : analysis and computations, ISSN 2194-041X, 2018, Volume 6, Issue 4, pp. 618 - 689

We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space...

Computational Mathematics and Numerical Analysis | 60G20 | 60B11 | Dual of a nuclear space | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | Computational Science and Engineering | Stochastic evolution equations | Cylindrical martingale-valued measures | Stochastic integrals | Numerical Analysis | 60H05 | 60H15 | Partial Differential Equations | LOCALLY CONVEX-SPACES | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATION | LANGEVIN-EQUATIONS | STATISTICS & PROBABILITY | OPERATORS | Mathematics - Probability

Computational Mathematics and Numerical Analysis | 60G20 | 60B11 | Dual of a nuclear space | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | Computational Science and Engineering | Stochastic evolution equations | Cylindrical martingale-valued measures | Stochastic integrals | Numerical Analysis | 60H05 | 60H15 | Partial Differential Equations | LOCALLY CONVEX-SPACES | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATION | LANGEVIN-EQUATIONS | STATISTICS & PROBABILITY | OPERATORS | Mathematics - Probability

Journal Article

Applied categorical structures, ISSN 0927-2852, 2012, Volume 22, Issue 1, pp. 79 - 97

The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties...

28C20 | Mathematics | Theory of Computation | Point free measures | Boolean rings | 28A60 | Geometry | 16B50 | Convex and Discrete Geometry | Categorical geometry | Segal space | Locales | 03G30 | Mathematical Logic and Foundations | MATHEMATICS | Algebra | Beer

28C20 | Mathematics | Theory of Computation | Point free measures | Boolean rings | 28A60 | Geometry | 16B50 | Convex and Discrete Geometry | Categorical geometry | Segal space | Locales | 03G30 | Mathematical Logic and Foundations | MATHEMATICS | Algebra | Beer

Journal Article

Communications on Stochastic Analysis, ISSN 0973-9599, 2018, Volume 12, Issue 3, pp. 215 - 223

Journal Article

IEEE Transactions on Power Systems, ISSN 0885-8950, 05/2017, Volume 32, Issue 3, pp. 2254 - 2266

Buildings are candidates for providing flexible demand due to their high consumption and inherent thermal inertia. In the future, flexible demand side reserves...

Schedules | flexible demand | Nanoelectromechanical systems | Buildings | Pricing | congestion management | convex optimization | distribution grid | Data models | Power systems | Load modeling | Convex Optimization | Congestion Management | Flexible Demand | Distribution Grid | SYSTEM | RESOURCES | MANAGEMENT | STATE | SIMULATION | MICROGRIDS | ENGINEERING, ELECTRICAL & ELECTRONIC | SMART BUILDINGS | GENERATION | Data mining | Convex programming | Research | Demand | Reserves | Incentives | Tariffs | Energy distribution | Benchmarks | Congestion | Energy industry | Optimization | Free energy | Electric utilities | Convexity | Reserve requirements

Schedules | flexible demand | Nanoelectromechanical systems | Buildings | Pricing | congestion management | convex optimization | distribution grid | Data models | Power systems | Load modeling | Convex Optimization | Congestion Management | Flexible Demand | Distribution Grid | SYSTEM | RESOURCES | MANAGEMENT | STATE | SIMULATION | MICROGRIDS | ENGINEERING, ELECTRICAL & ELECTRONIC | SMART BUILDINGS | GENERATION | Data mining | Convex programming | Research | Demand | Reserves | Incentives | Tariffs | Energy distribution | Benchmarks | Congestion | Energy industry | Optimization | Free energy | Electric utilities | Convexity | Reserve requirements

Journal Article

SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2019, Volume 41, Issue 5, pp. A3152 - A3181

... available. We present several new families of extended integration formulas that contain such integrals and provide in a special case of our result the multivariate analogues of midpoint, trapezoidal, Hammer, and Simpson rules...

MATHEMATICS, APPLIED | approximation | cubature formulas | CONVEX | NUMERICAL-INTEGRATION | centroidal Voronoi tessellation | convexity | singularity of integrand | best error estimates | Numerical Analysis | Computer Science

MATHEMATICS, APPLIED | approximation | cubature formulas | CONVEX | NUMERICAL-INTEGRATION | centroidal Voronoi tessellation | convexity | singularity of integrand | best error estimates | Numerical Analysis | Computer Science

Journal Article