IEEE Transactions on Circuits and Systems I: Regular Papers, ISSN 1549-8328, 02/2014, Volume 61, Issue 2, pp. 542 - 551

This paper proposes an improved global optimization technique, named Hybrid Coupled Local Minimizers (HCLM), which is inspired on the method of coupled local...

Couplings | Asymptotic stability | Global optimization | Lagrange programming network | Newton-based trust region method | pulse-coupling | Programming | Stability analysis | Synchronization | Optimization | hybrid coupled local minimizers | Convergence | STABILITY | NEURAL-NETWORK | SYSTEMS | OPTIMIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Usage | Stability | Analysis | Innovations | Linear programming | Regression analysis | Mathematical optimization | Semiconductor chips | Optimization techniques | Algorithms | Distributed processing | Searching | Synchronism | Multilayer perceptrons | Strategy | Spreads | Joining

Couplings | Asymptotic stability | Global optimization | Lagrange programming network | Newton-based trust region method | pulse-coupling | Programming | Stability analysis | Synchronization | Optimization | hybrid coupled local minimizers | Convergence | STABILITY | NEURAL-NETWORK | SYSTEMS | OPTIMIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Usage | Stability | Analysis | Innovations | Linear programming | Regression analysis | Mathematical optimization | Semiconductor chips | Optimization techniques | Algorithms | Distributed processing | Searching | Synchronism | Multilayer perceptrons | Strategy | Spreads | Joining

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 04/2017, Volume 153, pp. 294 - 310

It is well known that an integral of the Calculus of Variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents...

Anisotropic growth condition | Non-coercive functional | Local boundedness | INTEGRALS | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MINIMA | VARIATIONAL-PROBLEMS | NONSTANDARD GROWTH | ELLIPTIC-EQUATIONS | FUNCTIONALS | Anisotropy

Anisotropic growth condition | Non-coercive functional | Local boundedness | INTEGRALS | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MINIMA | VARIATIONAL-PROBLEMS | NONSTANDARD GROWTH | ELLIPTIC-EQUATIONS | FUNCTIONALS | Anisotropy

Journal Article

SIAM Journal on Imaging Sciences, 2013, Volume 6, Issue 2, pp. 904 - 937

We have an M x N real-valued arbitrary matrix A (e.g. a dictionary) with M Asymptotically level stable functions | Non-convex nonsmooth minimization | Perturbation analysis | Uniqueness of the solution | Variational methods | regularization | L | Quadratic programming | Underdetermined linear systems | Solution analysis | Strict minimizers | Global minimizers | Sparse recovery | Local minimizers | Signal and Image Processing | Mathematics | Numerical Analysis | Computer Science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 2, p. 123838

In this paper we consider a class of non-uniformly elliptic integral functionals and we prove the local boundedness of the quasi-minimizers. Our approach is...

Non-uniformly elliptic functionals | Local boundedness | Regularity of quasi-minimizers | Caccioppoli-type inequality

Non-uniformly elliptic functionals | Local boundedness | Regularity of quasi-minimizers | Caccioppoli-type inequality

Journal Article

JOURNAL OF FUNCTIONAL ANALYSIS, ISSN 0022-1236, 05/2017, Volume 272, Issue 9, pp. 3946 - 3964

We prove that a local minimizer of the Ginzburg Landau energy in R-3 satisfying the condition rim inf (R ->infinity) E(u(i)B(R))/R ln R < 2 pi must be...

MATHEMATICS | DIMENSION | PROPERTY | GIORGI | Ginzburg Landau Energy | ASYMPTOTICS | EQUATION | Local minimizers | CONJECTURE

MATHEMATICS | DIMENSION | PROPERTY | GIORGI | Ginzburg Landau Energy | ASYMPTOTICS | EQUATION | Local minimizers | CONJECTURE

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 05/2017, Volume 272, Issue 9, pp. 3946 - 3964

We prove that a local minimizer of the Ginzburg–Landau energy in R3 satisfying the condition liminfR→∞E(u;BR)RlnR<2π must be constant. The main tool is a new...

Local minimizers | Ginzburg–Landau Energy

Local minimizers | Ginzburg–Landau Energy

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123634

In this paper we consider a family of singularly perturbed non-homogeneous p-Laplacian problems ϵpdiv(k(x)|∇u|p−2∇u)+k(x)g(u)=0 in Ω⊂Rn subject to Neumann...

Transition layer | Γ-convergence | p-Laplacian | Local minimizer | Stability | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | POSITIVE SOLUTIONS | MATHEMATICS | ELLIPTIC PROBLEMS | BOUND-STATES | REGULARITY | GROWTH | Gamma-convergence

Transition layer | Γ-convergence | p-Laplacian | Local minimizer | Stability | EXISTENCE | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | POSITIVE SOLUTIONS | MATHEMATICS | ELLIPTIC PROBLEMS | BOUND-STATES | REGULARITY | GROWTH | Gamma-convergence

Journal Article

Optimization Letters, ISSN 1862-4472, 6/2013, Volume 7, Issue 5, pp. 1027 - 1033

An important property known, among other cases, for W 1,p (Ω) versus $${C^1(\overline{\Omega})}$$ -local minimizers of certain functions is extended to the...

Local minimizer | Computational Intelligence | 35J40 | Operations Research/Decision Theory | Numerical and Computational Physics | Elliptic boundary value problems | Mathematics | X -local minimizer | Critical point | 49K27 | Regularity | Optimization | X-local minimizer | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIPLICITY | LINEAR ELLIPTIC-EQUATIONS

Local minimizer | Computational Intelligence | 35J40 | Operations Research/Decision Theory | Numerical and Computational Physics | Elliptic boundary value problems | Mathematics | X -local minimizer | Critical point | 49K27 | Regularity | Optimization | X-local minimizer | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIPLICITY | LINEAR ELLIPTIC-EQUATIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 03/2018, Volume 168, pp. 81 - 109

In this paper we collect some new observations about periodic critical points and local minimizers of a nonlocal isoperimetric problem arising in the modeling...

Second variation | Ohta–Kawasaki energy | Local minimizers | SINGULAR PERTURBATIONS | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | ENERGY | STABILITY | Ohta-Kawasaki energy | NONLOCAL ISOPERIMETRIC PROBLEM | DENSITY | MATHEMATICS | DIBLOCK COPOLYMER PROBLEM | I-LIMIT | MORPHOLOGY | 2 DIMENSIONS

Second variation | Ohta–Kawasaki energy | Local minimizers | SINGULAR PERTURBATIONS | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | ENERGY | STABILITY | Ohta-Kawasaki energy | NONLOCAL ISOPERIMETRIC PROBLEM | DENSITY | MATHEMATICS | DIBLOCK COPOLYMER PROBLEM | I-LIMIT | MORPHOLOGY | 2 DIMENSIONS

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 5/2006, Volume 66, Issue 5, pp. 1632 - 1648

We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This...

Local minimum | Histograms | Algorithms | Approximation | Initial guess | Geometric shapes | Eigenfunctions | Mathematical functions | Mathematical minima | Segmentation | Denoising | denoising | MATHEMATICS, APPLIED | ABSOLUTE NORM | VARIATIONAL APPROACH | APPROXIMATION | FILTERS | segmentation | NOISE | OUTLIERS

Local minimum | Histograms | Algorithms | Approximation | Initial guess | Geometric shapes | Eigenfunctions | Mathematical functions | Mathematical minima | Segmentation | Denoising | denoising | MATHEMATICS, APPLIED | ABSOLUTE NORM | VARIATIONAL APPROACH | APPROXIMATION | FILTERS | segmentation | NOISE | OUTLIERS

Journal Article

IEEE Transactions on Evolutionary Computation, ISSN 1089-778X, 06/2004, Volume 8, Issue 3, pp. 211 - 224

This paper presents approaches for effectively computing all global minimizers of an objective function. The approaches include transformations of the...

Stochastic processes | Optimization methods | Genetic programming | Orbits | Mathematics | Particle swarm optimization | Game theory | Computational complexity | Least squares methods | stretching technique | STABILITY | detecting all minimizers | ALGORITHM | FILLED FUNCTION-METHOD | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | dynamical systems | PERIODIC-ORBITS | NONLINEAR MAPPINGS | periodic orbits | Nash equilibria | LOCAL MINIMA | deflection technique | CONVERGENCE | SYSTEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | particle swarm optimization (PSO) | SELECTION | Deflection | Computation | Mathematical analysis | Benchmarking | Mathematical models | Transformations | Dynamical systems | Optimization

Stochastic processes | Optimization methods | Genetic programming | Orbits | Mathematics | Particle swarm optimization | Game theory | Computational complexity | Least squares methods | stretching technique | STABILITY | detecting all minimizers | ALGORITHM | FILLED FUNCTION-METHOD | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | dynamical systems | PERIODIC-ORBITS | NONLINEAR MAPPINGS | periodic orbits | Nash equilibria | LOCAL MINIMA | deflection technique | CONVERGENCE | SYSTEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | particle swarm optimization (PSO) | SELECTION | Deflection | Computation | Mathematical analysis | Benchmarking | Mathematical models | Transformations | Dynamical systems | Optimization

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 12/2018, Volume 177, pp. 254 - 269

We consider variational integral functionals ∫Ωg(x,u(x),Du(x))dx,where Ω is a bounded open subset in Rn and the integrand g(x,s,ξ)=f(x,ξ)+b(x)s is not...

Global boundedness | Anisotropic growth conditions | EXISTENCE | MATHEMATICS, APPLIED | INTEGRABILITY | VECTOR-VALUED MINIMIZERS | DIFFERENTIABILITY | NONSTANDARD GROWTH-CONDITIONS | PHASE VARIATIONAL INTEGRALS | NONLINEAR ELLIPTIC-SYSTEMS | MATHEMATICS | CONTINUITY | REGULARITY | LOCAL BOUNDEDNESS

Global boundedness | Anisotropic growth conditions | EXISTENCE | MATHEMATICS, APPLIED | INTEGRABILITY | VECTOR-VALUED MINIMIZERS | DIFFERENTIABILITY | NONSTANDARD GROWTH-CONDITIONS | PHASE VARIATIONAL INTEGRALS | NONLINEAR ELLIPTIC-SYSTEMS | MATHEMATICS | CONTINUITY | REGULARITY | LOCAL BOUNDEDNESS

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2018, Volume 178, Issue 3, pp. 699 - 725

We consider polyconvex functionals of the Calculus of Variations defined on maps from the three-dimensional Euclidean space into itself. Counterexamples show...

Polyconvex | 35J50 | Minimizer | Local | Mathematics | Theory of Computation | Optimization | Bounded | 49N60 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Integral | Applications of Mathematics | Engineering, general | EXISTENCE | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | VECTOR-VALUED MINIMIZERS | NONLINEAR ELASTICITY | DIMENSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VARIATIONAL INTEGRALS | MODEL PROBLEM | FUNCTIONALS | PARTIAL REGULARITY | GROWTH-CONDITIONS | Euclidean geometry | Euclidean space | Functionals | Calculus of variations

Polyconvex | 35J50 | Minimizer | Local | Mathematics | Theory of Computation | Optimization | Bounded | 49N60 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Integral | Applications of Mathematics | Engineering, general | EXISTENCE | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | VECTOR-VALUED MINIMIZERS | NONLINEAR ELASTICITY | DIMENSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VARIATIONAL INTEGRALS | MODEL PROBLEM | FUNCTIONALS | PARTIAL REGULARITY | GROWTH-CONDITIONS | Euclidean geometry | Euclidean space | Functionals | Calculus of variations

Journal Article

Journal of Elasticity, ISSN 0374-3535, 10/2018, Volume 133, Issue 1, pp. 73 - 103

The uniqueness of absolute minimizers of the energy of a compressible, hyperelastic body subject to a variety of dead-load boundary conditions in two and three...

Energy minimizers | Nonuniqueness | Uniform polyconvexity | 35A02 | Classical Mechanics | Uniqueness | 35J57 | Physics | 49J40 | 74G65 | Strict polyconvexity | 74G30 | Automotive Engineering | Equilibrium solutions | Finite elasticity | Nonlinear elasticity | 74B20 | Strongly polyconvex | STABILITY | MATERIALS SCIENCE, MULTIDISCIPLINARY | MULTIDIMENSIONAL CALCULUS | 3-DIMENSIONAL ELASTICITY | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | QUASICONVEXITY | DISPLACEMENTS | STRONG LOCAL MINIMA | DEFORMATIONS | PARTIAL REGULARITY | Hypotheses | Compressibility | Flux density | Elasticity | Equilibrium equations | Nonlinear programming

Energy minimizers | Nonuniqueness | Uniform polyconvexity | 35A02 | Classical Mechanics | Uniqueness | 35J57 | Physics | 49J40 | 74G65 | Strict polyconvexity | 74G30 | Automotive Engineering | Equilibrium solutions | Finite elasticity | Nonlinear elasticity | 74B20 | Strongly polyconvex | STABILITY | MATERIALS SCIENCE, MULTIDISCIPLINARY | MULTIDIMENSIONAL CALCULUS | 3-DIMENSIONAL ELASTICITY | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | QUASICONVEXITY | DISPLACEMENTS | STRONG LOCAL MINIMA | DEFORMATIONS | PARTIAL REGULARITY | Hypotheses | Compressibility | Flux density | Elasticity | Equilibrium equations | Nonlinear programming

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 06/2017, Volume 272, Issue 11, pp. 4513 - 4587

In this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning C1-extremals at which the second variation is strictly...

Quasiconvexity at the boundary | Sufficient conditions | Boundary regularity | Strong local minimizers | MINIMA | CALCULUS | QUASI-CONVEX INTEGRALS | NONLINEAR ELLIPTIC-SYSTEMS | MATHEMATICS | CONTINUITY | QUASICONVEXITY | LOWER SEMICONTINUITY | SUBQUADRATIC GROWTH | MULTIPLE INTEGRALS | VARIATIONAL INTEGRALS | Mathematics - Analysis of PDEs

Quasiconvexity at the boundary | Sufficient conditions | Boundary regularity | Strong local minimizers | MINIMA | CALCULUS | QUASI-CONVEX INTEGRALS | NONLINEAR ELLIPTIC-SYSTEMS | MATHEMATICS | CONTINUITY | QUASICONVEXITY | LOWER SEMICONTINUITY | SUBQUADRATIC GROWTH | MULTIPLE INTEGRALS | VARIATIONAL INTEGRALS | Mathematics - Analysis of PDEs

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2015, Volume 166, Issue 1, pp. 1 - 22

The energy integral of the calculus of variations, which we consider in this paper, has a limit behavior when the maximum exponent $$q$$ q , in the growth...

35J60 | Quasi-minimizer | Mathematics | Theory of Computation | Local boundedness | 35J25 | Optimization | Anisotropic growth conditions | 49N60 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Non-coercive functional | EXISTENCE | MATHEMATICS, APPLIED | HOLDER CONTINUITY | ANISOTROPIC P | CALCULUS | INTEGRALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | ELLIPTIC-EQUATIONS | Anisotropy | Studies | Mathematical analysis | Calculus of variations | Thresholds | Integrals | Texts | Estimates | Regularity

35J60 | Quasi-minimizer | Mathematics | Theory of Computation | Local boundedness | 35J25 | Optimization | Anisotropic growth conditions | 49N60 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Non-coercive functional | EXISTENCE | MATHEMATICS, APPLIED | HOLDER CONTINUITY | ANISOTROPIC P | CALCULUS | INTEGRALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | ELLIPTIC-EQUATIONS | Anisotropy | Studies | Mathematical analysis | Calculus of variations | Thresholds | Integrals | Texts | Estimates | Regularity

Journal Article

Mathematical Programming, ISSN 0025-5610, 7/2019, Volume 176, Issue 1, pp. 39 - 67

Many optimization algorithms converge to stationary points. When the underlying problem is nonconvex, they may get trapped at local minimizers or stagnate near...

Nonconvex optimization | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Global optimality | Mathematical Methods in Physics | 49M30 | R-local minimizer | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Run-and-Inspect Method | Global minimum | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CUBIC-REGULARIZATION | ALGORITHM | Mathematical optimization | Methods | Algorithms | Nonlinear programming | Saddle points | Optimization

Nonconvex optimization | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Global optimality | Mathematical Methods in Physics | 49M30 | R-local minimizer | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Run-and-Inspect Method | Global minimum | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CUBIC-REGULARIZATION | ALGORITHM | Mathematical optimization | Methods | Algorithms | Nonlinear programming | Saddle points | Optimization

Journal Article

18.
Full Text
HIGHER INTEGRABILITY OF MINIMIZERS OF DEGENERATE FUNCTIONALS IN CARNOT-CARATHEODORY SPACES

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, ISSN 1239-629X, 2020, Volume 45, Issue 1, pp. 293 - 303

In this paper, we prove a higher integrability result for the horizontal gradient of a minimizer of a functional of the type I(Omega, u) = integral(Omega)...

WEIGHTED POINCARE | MATHEMATICS | A(p) weights | Hormander vector fields | LOCAL BOUNDEDNESS | regularity | SOBOLEV INEQUALITIES

WEIGHTED POINCARE | MATHEMATICS | A(p) weights | Hormander vector fields | LOCAL BOUNDEDNESS | regularity | SOBOLEV INEQUALITIES

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2017, Volume 154, pp. 7 - 24

We study the local regularity of vectorial minimizers of integral functionals with standard p-growth. We assume that the non-homogeneous densities are...

Regularity of minimizers | [formula omitted]-growth | Asymptotic convexity | Secondary | p-growth | Primary | EXISTENCE | P-Q GROWTH | MATHEMATICS, APPLIED | HOLDER CONTINUITY | SOBOLEV COEFFICIENTS | LOCAL MINIMIZERS | INFINITY | MATHEMATICS | REGULARITY | HIGHER DIFFERENTIABILITY | NONCONVEX VARIATIONAL PROBLEM | FUNCTIONALS

Regularity of minimizers | [formula omitted]-growth | Asymptotic convexity | Secondary | p-growth | Primary | EXISTENCE | P-Q GROWTH | MATHEMATICS, APPLIED | HOLDER CONTINUITY | SOBOLEV COEFFICIENTS | LOCAL MINIMIZERS | INFINITY | MATHEMATICS | REGULARITY | HIGHER DIFFERENTIABILITY | NONCONVEX VARIATIONAL PROBLEM | FUNCTIONALS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 1, pp. 27 - 56

We study H1 versus C1 local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some...

[formula omitted] versus [formula omitted] local minimizers | Hénon type weights | Critical exponents | Spaces of symmetric functions | C 1 versus H 1 local minimizers | DIFFERENTIAL EQUATIONS | DIRICHLET PROBLEMS | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | C-1 versus H-1 local minimizers | NONLINEAR EIGENVALUE PROBLEMS | POSITIVE SOLUTIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | HENON EQUATION | Henon type weights | CRITICAL SOBOLEV EXPONENTS | GROUND-STATES | Mathematics - Analysis of PDEs

[formula omitted] versus [formula omitted] local minimizers | Hénon type weights | Critical exponents | Spaces of symmetric functions | C 1 versus H 1 local minimizers | DIFFERENTIAL EQUATIONS | DIRICHLET PROBLEMS | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | C-1 versus H-1 local minimizers | NONLINEAR EIGENVALUE PROBLEMS | POSITIVE SOLUTIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | HENON EQUATION | Henon type weights | CRITICAL SOBOLEV EXPONENTS | GROUND-STATES | Mathematics - Analysis of PDEs

Journal Article