Multivariate Bonferroni-type inequalities and optimality

Bonferroni-type inequalities and binomially bounded functions

We present a unified approach to an important subclass of Bonferroni-type inequalities by considering so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By appropriately choosing this function, several well-known and new results are deduced.

Support Approximations Using Bonferroni-Type Inequalities

Upper Bounds for Bivariate Bonferroni-type Inequalities Using Consecutive Events

Let A1, A2, . . . , Am and B1, B2, . . . , Bn be two sequences of events on the same probability space. Let X = Xm(A) and Y = Yn(B), respectively, denote the numbers of those Ai’s and Bj ’s which occur. We establish new bivariate Bonferroni-type inequalities using consecutive events and deduce a known result.

BONFERRONI-TYPE INEQUALITIES; CHEBYSHEV-TYPE INEQUALITIES FOR THE DISTRIBUTIONS ON [0, n]

Abs t rac t . An elementary "majorant-minorant method" to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1 , . . . , n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known resuits are ...

Sequential Optimality Conditions and Variational Inequalities

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...