This paper indicates that the filled function which appeared in one of the papers by Y. L. Shang et al. 2007 is also a tunneling function; that is, we prove that under some general assumptions this function has the characters of both tunneling function and filled function. A solution algorithm based on this T-F function is given and numerical tests from test functions show that our T-F function...

To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a...

We present a computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model of diblock copolymers. The model is a fourth-order parabolic partial differential equation subject to homogeneous Neumann boundary conditions, which contains as a special case the celebrated Cahn-Hilliard equation. While the attractor structure of the latter model is completely understood...

A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, optimized. This allows us to handle topology changes and multiple materials. We prove continuity differentiability we establish existence global minimizer our optimization problem. further derive first-order necessary optimality conditions for local minimizers. Moreover, probl...

<p style='text-indent:20px;'>In this paper we find curves minimizing the elastic energy among whose length is fixed and ends are pinned. Applying shooting method, can identify all critical points explicitly determine which curve global minimizer. As a result show that consist of wavelike elasticae minimizers do not have any loops or interior inflection points.</p>

where α = max(|D(ui)|, |D(uj)|)+ ; is a small positive number. For notational simplicity, we denoteD(xi) = D(ui)xi, V (xi, xj) = V (ui, uj)xixj , V̂ (xi, xj) = V̂ (ui, uj)xixj , andR(xi, xj) = R(ui, uj)xixj . Lemma 1. If X∗ is the global optimum of E(X),R(xi, xj) < To,∀ xi ∼ xj , xi, xj ∈ X∗. Proof. If there exists a pair xi ∼ xj , xi, xj ∈ X∗ such thatR(xi, xj) ≥ To, then E(X∗) > 0 = E(0) (5) wh...

INTRODUCTION Laparoscopic adjustable gastric banding (LAGB) is a method frequently used for treating obesity. It requires periodic band regulation associated with the need for port puncture. However, there is always a substantial risk of port rotation. AIM This publication presents a solution of the problem for a MiniMizer Extra band. MATERIAL AND METHODS One thousand one hundred and twenty...

We consider kernel based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables. We find that the risk minimizer remains unchanged if we constrain the risk minimization to hypothesis spaces induced by suitable kernel functions. We show that not all kernel ...

We focus the minimization of 1D free discontinuity problem with second order energy dependent on jump integrals but not on the cardinality of the discontinuity set, in the framework of L∞ load. The related energies are not lower semi continuous in BH. Nevertheless we show that if a safe load condition is fulfilled then minimizers exist and they belong actually to SBH, say their second derivativ...

The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a global minimizer of the error. Previous work showed that a global solution could be obtained for continuous PWA maps with a worst-case complexity exponential i...