2 citations · 2 across the 2 of their papers we have counts for
10 papers
Error bounds for overdetermined and underdetermined generalized centred simplex gradients
Warren Hare, Gabriel Jarry--Bolduc, Chayne Planiden
Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of poi…
Parametrically prox-regular functions
Warren Hare, Chayne Planiden
Prox-regularity is a generalization of convexity that includes all C2, lower-C2, strongly amenable and primal-lower-nice functions. The study of prox-regular functions provides ins…
The NC-proximal average for multiple functions
Warren Hare, Chayne Planiden
The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now, it has been defined for two functi…
Some geometric properties of the solutions of complex multi-affine polynomials of degree three
Chayne Planiden, Hristo Sendov
In this paper, we consider complex polynomials of degree three with distinct zeros and their polarization ((z1,z2,z3) with three complex variables. We show, through elementary mean…
Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions
Chayne Planiden, Xianfu Wang
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions a…
Epiconvergence, the Moreau envelope and generalized linear-quadratic functions
Chayne Planiden, Xianfu Wang
This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the More…