28 citations · 29 across the 8 of their papers we have counts for
13 papers
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…
Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal Control Problems
C. Yalçın Kaya, Helmut Maurer
Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a…
A Generalized Multivariable Newton Method
Regina S. Burachik, Bethany I. Caldwell, C. Yalçın Kaya
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of t…
Observer Path Planning for Maximum Information
C. Yalçın Kaya
This paper is concerned with finding an optimal path for an observer, or sensor, moving at a constant speed, which is to estimate the position of a stationary target, using only be…
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…
Optimal Residuals and the Dahlquist Test Problem
Robert M. Corless, C. Yalcin Kaya, Robert H. C. Moir
We show how to compute the \emph{optimal relative backward error} for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of a general appr…
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…
Markov-Dubins Interpolating Curves
C. Yalçın Kaya
A realistic generalization of the Markov--Dubins problem, which is concerned with finding the shortest planar curve of constrained curvature joining two points with prescribed tang…
Markov-Dubins Path via Optimal Control Theory
C. Yalçın Kaya
Markov-Dubins path is the shortest planar curve joining two points with prescribed tangents, with a specified bound on its curvature. Its structure, as proved by Dubins in 1957 nea…