Convex Optimization with ALADIN

This paper presents novel convergence results for the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) in the context of distributed convex optimization. It is shown that ALADIN converges for a large class of convex optimization problems from any starting point to minimizers without needing line-search or other globalization routines. Under additional regularity assumptions, … Read more

Global Optimization in Hilbert Space

This paper proposes a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. … Read more

Lifted Collocation Integrators for Direct Optimal Control in ACADO Toolkit

This paper presents a class of efficient Newton-type algorithms for solving the nonlinear programs (NLPs) arising from applying a direct collocation approach to continuous time optimal control. The idea is based on an implicit lifting technique including a condensing and expansion step, such that the structure of each subproblem corresponds to that of the multiple … Read more

Efficient Symmetric Hessian Propagation for Direct Optimal Control

Direct optimal control algorithms first discretize the continuous-time optimal control problem and then solve the resulting finite dimensional optimization problem. If Newton type optimization algorithms are used for solving the discretized problem, accurate first as well as second order sensitivity information needs to be computed. This article develops a novel approach for computing Hessian matrices … Read more

An Augmented Lagrangian based Algorithm for Distributed Non-Convex Optimization

This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interpreted as prices, a concept … Read more

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a spatial branch-and-bound algorithm. A new operation, called lifting, is introduced which refines the control parameterization via a Gram-Schmidt orthogonalization … Read more

A lifting method for generalized semi-infinite programs based on lower level Wolfe duality

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be … Read more