We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals ...

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an ε-global minimizer is guaranteed. At each iteration k, the algorithm requires a (ρ(k),ε(k))-global minimizer of a bound constrained bi-objective subproblem, where as k→ ∞, ρ(k)→ 0 gives the constraint violation tolerance and ε(k)→ ε is the error bo...

In this paper, we discuss the global minimizers of a free energy for the superconducting thin films placed in a magnetic field hex below the lower critical field Hc1 or between Hc1 and the upper critical field Hc2 . For hex is near but smaller than Hc1 , we prove that the global minimizer having no vortex is unique. For Hc1 << hex << Hc2 , we prove that the density of the vortices of the global...

When a convex function f : D → R is disturbed by some nonlinear bounded perturbation p : D → R, the arising function f̃ = f + p is no more convex and its local minimizers are no more global minimizers. In order to get some similar properties for f̃ , we use a convexity modulus of f named h1 and its generalized inverse function h−1 1 , and show that f̃ is outer γ-convex for any γ ≥ γ∗ := h−1 1 ( 2 ...

This paper presents a new method for solving global optimization problems. We use a local technique based on the notion of discrete gradients for finding a cone of descent directions and then we use a global cutting angle algorithm for finding global minimum within the intersection of the cone and the feasible region. We present results of numerical experiments with well-known test problems and...

We have an M × N real-valued arbitrary matrix A (e.g. a dictionary) with M < N and data d describing the sought-after object with the help of A. This work provides an indepth analysis of the (local and global) minimizers of an objective function Fd combining a quadratic data-fidelity term and an l0 penalty applied to each entry of the sought after solution, weighted by a regularization paramete...

We have an M × N real-valued arbitrary matrix A (e.g. a dictionary) with M < N and data d describing the sought-after object with the help of A. This work provides an in-depth analysis of the (local and global) minimizers of an objective function Fd combining a quadratic data-fidelity term and an l0 penalty applied to each entry of the sought-after solution, weighted by a regularization paramet...

We have an M × N real-valued arbitrary matrix A (e.g. a dictionary) with M < N and data d describing the sought-after object with the help of A. This work provides an in-depth analysis of the (local and global) minimizers of an objective function Fd combining a quadratic data-fidelity term and an l0 penalty applied to each entry of the sought-after solution, weighted by a regularization paramet...

In this paper, an optimal shape design for an interfacial boundary between different media, through which sound propagates, is discussed. For example, designs for soundproof walls along high-speed train routes or highways, walls of concert halls, etc are included in the same category. For the above-mentioned problems, an algorithm to search for an optimal shape was proposed and tested numerical...