Focal Subfunctions and Second Order Differential Inequalities

Generalized Convex Functions and Second Order Differential Inequalities

Second-order cover inequalities

We introduce a new class of second-order cover inequalities whose members are generally stronger than the classical knapsack cover inequalities that are commonly used to enhance the performance of branch-and-cut methods for 0–1 integer programming problems. These inequalities result by focusing attention on a single knapsack constraint in addition to an inequality that bounds the sum of all var...

Harnack Inequality for Second Order Linear Ordinary Differential Inequalities

The Harnack Inequality is an important tool in the study of qualitative properties of solutions to elliptic and degenerate elliptic partial differential equations. Perhaps the first paper that discusses such an inequality for ordinary linear differential equations of second order is the article A Harnack Inequality for Ordinary Differential Equations [1]. The objective of this project was to ex...

Inequalities for Complex Linear Differential Systems of the Second Order.

where a, f3, y, 6 are complex valued functions of the real variable t. These functions are assumed to be of class C' on some interval, to _ t < T, where T may be c. We also restrict attention to the "general case" in which A = (6 a)2 + 40ry 5 0 and y $ 0 on this interval. The inequalities obtained are the best possible ones of their type and are especially adapted to the case in which a, ,B, y,...

Second-order Matrix Concentration Inequalities

Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies one of the sources of the dimensional term and exploits this insight to develop sharper matrix concentration inequalities. In particular, this analysis delive...