Differentially Private Mechanism for the Equiribrium Price under Quadratic Cost Functions and Quadratic Utility Functions

Half-quadratic cost functions for phase unwrapping.

We present a generic regularized formulation, based on robust half-quadratic regularization, for unwrapping noisy and discontinuous wrapped phase maps. Two cases are presented: the convex case and the nonconvex case. The unwrapped phase with the convex formulation is unique and robust to noise; however, the convex function solution deteriorates as a result of real discontinuities in phase maps....

Credit Cards Scoringwith Quadratic Utility Functions

The paper considers a general approach for classifying objects using mathematical programming algorithms. The approach is based on optimizing a utility function, which is quadratic in indicator parameters and is linear in control parameters (which need to be identified). Qualitative characteristics of the utility function, such as monotonicity in some variables, are included using additional co...

On the quadratic support of strongly convex functions

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

Quadratic Functions, Optimization, and Quadratic Forms

Groups with Quadratic-Non-Quadratic Dehn Functions

We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.