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math.OC2026
Interwoven SDP in Primal-Dual Proximal Splitting Methods for Adjustable Robust Convex Optimisation with SOS-Convex Polynomial Constraints
Neil D. Dizon, Bethany I. Caldwell, Vaithilingam Jeyakumar +1
We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined b…
math.OC2026
Best Approximation Optimal Control for Infeasible Double Integrator and Douglas--Rachford Algorithm
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya +2
We consider the problem of finding (in some sense) the best approximation control for an infeasible double integrator. The control function is constrained by upper and lower bounds…
math.OC2024
On the Douglas-Rachford and Peaceman-Rachford algorithms in the presence of uniform monotonicity and the absence of minimizers
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya +2
The Douglas-Rachford and Peaceman-Rachford algorithms have been successfully employed to solve convex optimization problems, or more generally find zeros of monotone inclusions. Re…