Abstract The purpose of this paper is to give a regularization variant of the inertial proximal point algorithm not only in an infinite-dimensional Banach space E, which is an uniformly smooth and uniformly convex, but also in its finite-dimensional approximations for finding a point in the nonempty intersection ∩i=1Ci, where N ≥ 1 is an integer and each Ci is assumed to be the fixed point set ...

In this paper, we design a novel alternating update method for solving a class of generalized bilinear programming problem, where each subproblem is regularized by a positive-definite proximal term to guarantee the convergence of the method. By using the tool of the variational inequality and the property of a monotonicity operator, its global convergence is analyzed and a worst-case O(1/t) con...

This paper investigates the value function, V , of a Mayer optimal control problem with the state equation given by a differential inclusion. First, we obtain an invariance property for the proximal and Fréchet subdifferentials of V along optimal trajectories. Then, we extend the analysis to the sub/superjets of V , obtaining new sensitivity relations of second order. By applying sensitivity an...

The problem of computing a maximum a posteriori (MAP) configuration is a central computational challenge associated with Markov random fields. There has been some focus on “tree-based” linear programming (LP) relaxations for the MAP problem. This paper develops a family of super-linearly convergent algorithms for solving these LPs, based on proximal minimization schemes using Bregman divergence...

1. Isolated kidneys taken from spontaneously hypertensive rats (SHR) and normotensive Wistar-Kyoto rats (WKY) were perfused over a range of perfusion pressures. 2. Lithium clearance was used as an index of proximal tubule sodium handling. 3. When the perfusate contained an oncotic agent (albumin, 6.7 g/dl) the SHR kidneys performed differently from the WKY kidneys with a reduction in inulin cle...

right of private property is of the most important individual rights of society that lies in the heart of private law. in islamic law protection of property as one of the five goals of fighhe, that is, protection of sagacity, religion, generation and self, is to be stipulated. based on article 140 of civil code the process of property acquisition is restricted to four cases. on the other hand, ...

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x, y) = f(x)+Q(x, y)+g(y), where f : Rn → R∪{+∞} and g : Rm → R∪{+∞} are proper lower semicontinuous functions, and Q : Rn × Rm → R is a smooth C function which couples the variables x and y. The algorithm can be viewed as a proximal regularization of the usual...

The nervous system of Hydra, a freshwater cnidaria, occurs as dispersed, or diffuse, nerve net throughout the animal. It is widely accepted that in a diffuse nervous system an external stimulus is conducted in all directions over the net. Here I report observations that hydra tentacles respond to feeding and wounding stimuli in a unidirectional manner. Upon contact of a tentacle with a brine sh...

We address the minimization of the sum of a proper, convex and lower semicontinuous with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The trajectory generated by the dynamical system is proved t...

Using a result linking convexity and irreducibility of matrix sets it is shown that the generalized spectral radius of a compact set of matrices is a strictly increasing function of the set in a very natural sense. As an application some consequences of this property in the area of time-varying stability radii are discussed. In particular, using the implicit function theorem sufficient conditio...