92 citations · 106 across the 19 of their papers we have counts for
18 papers · 1 filter
A Primal--Dual Penalty Algorithm and Optimal Control of the Double Integrator
Regina S. Burachik, C. Yalçın Kaya, Xuemei Liu
We investigate the behaviour of a primal--dual penalty scheme applied to all possible instances, i.e., boundary conditions, of an optimal control problem involving the double integ…
Best Approximation Optimal Control for Infeasible Double Integrator and Douglas--Rachford Algorithm
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya +1
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…
Infeasible and Critically Feasible Optimal Control
Regina S. Burachik, C. Yalçın Kaya, Walaa M. Moursi
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the o…
Douglas-Rachford Algorithm for Control- and State-constrained Optimal Control Problems
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya
We consider the application of the Douglas-Rachford (DR) algorithm to solve linear-quadratic (LQ) control problems with box constraints on the state and control variables. We split…
A primal--dual algorithm as applied to optimal control problems
Regina S. Burachik, C. Yalçın Kaya, Xuemei Liu
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our g…
Optimal Control Duality and the Douglas-Rachford Algorithm
Regina S. Burachik, Bethany I Caldwell, C. Yalçın Kaya +1
We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas-Rachford (DR…
An Inexact Deflected Subgradient Algorithm in Infinite Dimensional spaces
Regina S. Burachik, Xuemei Liu
We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type o…
Douglas--Rachford algorithm for control-constrained minimum-energy control problems
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya
Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal…
Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems
Hoa T. Bui, Regina S. Burachik, Evgeni A. Nurminski +1
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible po…
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…
Sparse Network Optimization for Synchronization
Regina S. Burachik, Alexander C. Kalloniatis, C. Yalçın Kaya
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied usi…
On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections
Heinz H. Bauschke, Regina S. Burachik, Daniel B. Herman +1
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditi…
Steklov Convexification and a Trajectory Method for Global Optimization of Multivariate Quartic Polynomials
Regina S. Burachik, C. Yalçın Kaya
The Steklov function is defined to average a continuous function at each point of its domain by using a window of size given by . It has traditionally been…
Algorithms for Generating Pareto Fronts of Multi-objective Integer and Mixed-Integer Programming Problems
Regina S. Burachik, C. Yalçın Kaya, M. Mustafa Rizvi
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front cha…
Steklov Regularization and Trajectory Methods for Univariate Global Optimization
Orhan Arıkan, Regina S. Burachik, C. Yalçın Kaya
We introduce a new regularization technique, using what we refer to as the Steklov regularization function, and apply this technique to devise an algorithm that computes a global m…
Constraint Splitting and Projection Methods for Optimal Control of Double Integrator
Heinz H. Bauschke, Regina S. Burachik, C. Yalçın Kaya
We consider the minimum-energy control of a car, which is modelled as a point mass sliding on the ground in a fixed direction, and so it can be mathematically described as the doub…
A projection algorithm for non-monotone variational inequalities
Regina S. Burachik, R. Díaz Millán
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assump…
An additive subfamily of enlargements of a maximally monotone operator
Regina Burachik, Juan Enrique Martínez-Legaz, Mahboubeh Rezaie +1
We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute…