30 citations · 80 across the 16 of their papers we have counts for
20 papers
Tight error bounds for log-determinant cones without constraint qualifications
Ying Lin, Scott B. Lindstrom, Bruno F. Lourenço +1
In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspecti…
Generalized power cones: optimal error bounds and automorphisms
Ying Lin, Scott B. Lindstrom, Bruno F. Lourenço +1
Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until recently, provable error bounds in the absence of constraint qualifications were unatta…
Optimal error bounds in the absence of constraint qualifications with applications to the -cones and beyond
Scott B. Lindstrom, Bruno F. Lourenço, Ting Kei Pong
We prove tight Hölderian error bounds for all -cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured; moreover, they illumin…
The Projected Polar Proximal Point Algorithm Converges Globally
Scott B. Lindstrom
Friedlander, Macêdo, and Pong recently introduced the projected polar proximal point algorithm (P4A) for solving optimization problems by using the closed perspective transforms of…
Generalized Bregman envelopes and proximity operators
Regina S. Burachik, Minh N. Dao, Scott B. Lindstrom
Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, B…
Error bounds, facial residual functions and applications to the exponential cone
Scott B. Lindstrom, Bruno F. Lourenço, Ting Kei Pong
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or eve…
Centering Projection Methods for Wavelet Feasibility Problems
Neil Dizon, Jeffrey Hogan, Scott B. Lindstrom
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and…
A Note on Cores and Quasi Relative Interiors in Partially Finite Convex Programming
Scott B. Lindstrom
The problem of minimizing an entropy functional subject to linear constraints is a useful example of partially finite convex programming. In the 1990s, Borwein and Lewis provided b…
Computable Centering Methods for Spiraling Algorithms and their Duals, with Motivations from the theory of Lyapunov Functions
Scott B. Lindstrom
For many problems, some of which are reviewed in the paper, popular algorithms like Douglas--Rachford (DR), ADMM, and FISTA produce approximating sequences that show signs of spira…
Circumcentering Reflection Methods for Nonconvex Feasibility Problems
Neil Dizon, Jeffrey Hogan, Scott B. Lindstrom
Recently, circumcentering reflection method (CRM) has been introduced for solving the feasibility problem of finding a point in the intersection of closed constraint sets. It is cl…
The Generalized Bregman Distance
Regina S. Burachik, Minh N. Dao, Scott B. Lindstrom
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a prop…
Phase Portraits of Hyperbolic Geometry
Scott B. Lindstrom, Paul Vrbik
Phase plotting is a useful way of visualising functions on complex space. We reinvent the method in the context of hyperbolic geometry, and we use it to plot functions on various r…
Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples
R. Díaz Millán, Scott B. Lindstrom, Vera Roshchina
We focus on the convergence analysis of averaged relaxations of cutters, specifically for variants that---depending upon how parameters are chosen---resemble \emph{alternating proj…
Survey: Sixty Years of Douglas--Rachford
Scott B. Lindstrom, Brailey Sims
The Douglas--Rachford method is a splitting method frequently employed for finding zeroes of sums of maximally monotone operators. When the operators in question are normal cones o…
Proximal Averages for Minimization of Entropy Functionals
Heinz H. Bauschke, Scott B. Lindstrom
In their 2016 article `Meetings with Lambert and Other Special Functions in Optimization and Analysis', Borwein and Lindstrom considered the minimization of an entrop…
VADU 2018 Open Problem Session
Bui Thi Hoa, Scott Lindstrom, Vera Roshchina
We state the problems discussed in the open problem session at Variational Analysis Down Under (VADU2018) conference held in honour of Prof. Asen Dontchev's 70th birthday on 19--21…
The Douglas--Rachford algorithm for a hyperplane and a doubleton
Heinz H. Bauschke, Minh N. Dao, Scott B. Lindstrom
The Douglas--Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, t…
Application of projection algorithms to differential equations: boundary value problems
Bishnu P. Lamichhane, Scott B. Lindstrom, Brailey Sims
The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for…
Regularizing with Bregman-Moreau envelopes
Heinz H. Bauschke, Minh N. Dao, Scott B. Lindstrom
Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (also known as the proximal mapping), appeared in 1965. The Moreau envelope of…
Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres
Jonathan M. Borwein, Scott B. Lindstrom, Brailey Sims +2
We expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellips…