6 citations · 14 across the 18 of their papers we have counts for
9 papers · 1 filter
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…
The chain rule for VU-decompositions of nonsmooth functions
Warren Hare, Chayne Planiden, Claudia Sagastizábal
In Variational Analysis, VU-theory provides a set of tools that is helpful for understanding and exploiting the structure of nonsmooth functions. The theory takes advantage of the…
Conditions for the existence, identification and calculus rules of the threshold of prox-boundedness
Chayne Planiden
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the ex…
A proximal average for prox-bounded functions
Jiawei Chen, Xianfu Wang, Chayne Planiden
In this work, we construct a proximal average for two prox-bounded functions, which recovers the classical proximal average for two convex functions. The new proximal average trans…
A derivative-free -algorithm for convex finite-max problems
Warren Hare, Chayne Planiden, Claudia Sagastizábal
The -algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain -sp…