We propose a class of self-adaptive proximal point methods suitable for degenerate optimization problems where multiple minimizers may exist, or where the Hessian may be singular at a local minimizer. If the proximal regularization parameter has the form μ(x)= β‖∇f (x)‖η where η ∈ [0,2) and β > 0 is a constant, we obtain convergence to the set of minimizers that is linear for η= 0 and β suffici...

We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some kn...

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

Before any of the eleven possible quinones of azulene were known, predictions were made about their proper— ties on the basis of Hickel, MINDO/3, PPP and ab initio SCF (STO—3G) calculations (3). Four unsubstituted quinones of azulene have now been prepared, and the experimental results obtained so far provide information regarding their stability, reduction potentials, cycloadditions with cyclo...

We provide an iterative method for finding a common solution of a finite family of equilibrium problems and of a fixed point problem, and prove its strong convergence. Our method extends an implicit method of Colao, et al. (Nonlinear Anal. 71 (2009), no. 7-8, 2708-2715) to an explicit method (in the case of a single nonexpansive mapping).

in the recent paper, one of the numerical methods without element, for static analysis of thin plates displacement based on classical plates theory (cpt), has been presented. in this method, the domain of problem solving is shown only by the means of a set of nodes, and there is no need to any mesh scheme or element. one of the kinds of element free methods used here is the radial point interpo...

For several years, the financial services industry has discovered the opportunities of different channels like the Internet, call-centers, WAP etc. Many banks built up separate direct banks focusing exclusively on the Internet and/or call-centers. Only recently, some banks started to reintegrate the direct banks with their traditional brickand-mortar banks in order to offer services over severa...

In the context of EDEMOI -a French national project that proposed the use of semiformal and formal methods to infer the consistency and robustness of aeronautical regulations through the analysis of faithfully representative modelsa methodology had been suggested (and applied) to different (safety and security-related) aeronautical regulations. This paper summarizes the preliminary results of t...