Dai, L. 2016. Identification using Convexification and Recursion. Uppsala Dissertations from the Faculty of Science and Technology 123. 101 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9507-7. System identification studies how to construct mathematical models for dynamical systems from the input and output data, which finds applications in many scenarios, such as predicting futu...

Convex representations of shapes have several nice properties that can be exploited to generate efficient geometric algorithms. At the same time, extending algorithms from convex to non-convex shapes is non-trivial and often leads to more expensive solutions. An alternative and sometimes more efficient solution is to transform the non-convex problem into a collection of convex problems using a ...

In this paper, we propose a new method that produces new forms of tight convex underestimators for twice continuously differentiable nonconvex functions. The algorithm generalizes the main ideas used in aBB. The key idea is to determine a new convexification function that is able to handle the off-diagonal elements of the Hessian matrix of the original nonconvex function. The new convexificatio...

Abstract—We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial netw...

In this paper, we develop a convexification tool that enables the construction of convex hulls for orthogonal disjunctive sets using convex extensions and disjunctive programming techniques. A distinguishing feature of our technique is that, unlike most applications of disjunctive programming, it does not require the introduction of new variables in the relaxation. We develop and apply a toolbo...

Abstract—We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial netw...

Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not of the objective function as most bund...

Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates...