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Parametric Active Set Methods (PASM) are a relatively new class of methods to solve convex Quadratic Programming (QP) problems. They are based on tracing the solution along a linear homotopy between a QP with known solution and the QP to be solved. We explicitly identify numerical challenges in PASM and develop strategies to meet these challenges. To(More)
We investigate an iterative method for the solution of time-periodic parabolic PDE constrained optimization problems. It is an inexact Sequential Quadratic Programming (iSQP) method based on the Newton-Picard approach. We present and analyze a linear quadratic model problem and prove optimal mesh-independent convergence rates. Additionally, we propose a(More)
" Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques " which has been archived on the university repository Lirias (https://lirias.kuleuven.be/) of the Katholieke Universiteit Leuven. (2011). Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques. Numerical Algorithms, 57, 217-233. Abstract In(More)
In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such(More)
We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a(More)
We describe trlib, a library that implements a variant of Gould's Generalized Lanczos method (Gould et al. in SIAM J. Opt. 9(2), 504–525, 1999) for solving the trust region problem. Our implementation has several distinct features that set it apart from preexisting ones. We implement both conjugate gradient (CG) and Lanczos iterations for assembly of Krylov(More)
For the widespread application of nonlinear model-predictive control (NMPC) in the chemical industry, the computational effort that is required for the solution of the underlying resulting nonlinear dynamic optimization problems is a major obstacle. For complex process models and long prediction and control horizons, the computation times lead to large(More)