We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

Abstract We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by direct method of moving planes. first prove several important theorems, such as asymptotic maximum principle, narrow region principle strong for antisymmetric functions, which are critical factors in process Then, we further derive some properties radial solution to a unit ball. These con...

This paper proposes an initialization approach for parameter estimation problems (PEPs) involving parameter-affine dynamic models. By using the state measurements, the nonconvex PEP is modified such that a convex approximation to the original PEP is obtained. The modified problem is solved by vailable online 5 November 2009 eywords: arameter estimation ultiple shooting onvex optimization convex...

The problem of utilizing undesirable (bad) outputs in DEA models often need replacing the assumption of free disposability of outputs by weak disposability of outputs. The Kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs. Also, there are some specific features of non-radial data envelopment analysis (DEA...

We consider Backward Stochastic Diierential Equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coeecient which is Lipschitz-continuous in the state-and gains-processes, and convex in the gains-process. It is also shown that the minimal solution can be characterized as the unique so...

This work studies the convex relaxation approach to the left ventricle (LV) segmentation which gives rise to a challenging multi-region seperation with the geometrical constraint. For each region, we consider the global Bhattacharyya metric prior to evaluate a gray-scale and a radial distance distribution matching. In this regard, the studied problem amounts to finding three regions that most c...

In this article, we consider the focusing cubic nonlinear Schrödinger equation(NLS) in exterior domain outside of a convex obstacle ?3 with Dirichlet boundary conditions. We revisit scattering result below ground state Killip—Visan—Zhang [The NLS on domains three dimensions. Appl. Math. Res. Express. AMRX, 1, 146–180 (2016)] by utilizing method Dodson and Murphy [A new proof for 3d radial NLS. ...

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now the non-convex algorithms lack convergence guarantee from the initial solution to the global optimum. This paper aims to provide theoretical guarantee for sparse recovery via non-convex optimization. The concept of weak convexity is incorporated into...