We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between the directional derivatives of the objective function and its surrogate function vanishes when the number of iterations approaches infinity, which is a very...

Criteria containing a barrier function i.e., an unbounded function at the boundary of the feasible solution domain are frequently encountered in the optimization framework, in particular in interior point methods for constrained optimization. Barrier function has to be carefully handled in the optimization algorithm. When an iterative descent method is used for the minimization, a search along ...

This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between related sup-inf problems. The key assumption introduced in generalizes well-known Babuška–Brezzi condition. It based on condition defined for cones function spaces. also apply regularization method convenient solving derive com...

The direct simulation Monte Carlo (DSMC) method is one of the most popular numerical methods used to model rarefied gas environment flows. In order to predict the accuracy of a solution obtained by the DSMC method we have to be able to estimate its accuracy. In the work presented here we have developed a technique to estimate the numerical accuracy of the DSMC method. This paper presents a deri...

In this paper we investigate the Erdös/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been classically used to study this problem. We conjecture that a majorant for the spherical means suffices to prove the distance conjecture(s) in this setting. For a ...

We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H div space. In order to keep the estimate sharp, a procedure for the minimization of the majorant term with respect to the ux variable...

In this paper we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n 1 3 . The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0,∞), is a prototypical example. We focus on this example and explore different approaches to cons...