Nonlinear Optimization

Efficient search strategies for constrained multiobjective blackbox optimization

Categories Multi-Criteria Optimization, Nonlinear Optimization Tags ,

Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more

New Algorithms for maximizing the difference of convex functions

Categories Global Optimization, Global Optimization Applications, Nonlinear Optimization

Maximizing the difference of 2 convex functions over a convex feasible set (the so called DCA problem) is a hard problem. There is a large number of publications addressing this problem. Many of them are variations of widely used DCA algorithm [20]. The success of this algorithm to reach a good approximation of a global … Read more

Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. … Read more

qpBAMM: a parallelizable ADMM approach for block-structured quadratic programs

Categories Convex Optimization, Quadratic Programming Tags , , ,

Block-structured quadratic programs (QPs) frequently arise in the context of the direct approach to solving optimal control problems. For successful application of direct optimal control algorithms to many real-world problems it is paramount that these QPs can be solved efficiently and reliably. Besides interior-point methods and active-set methods, ADMM-based quadratic programming approaches have gained popularity. … Read more

NonOpt: Nonconvex, Nonsmooth Optimizer

Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

NonOpt, a C++ software package for minimizing locally Lipschitz objective functions, is presented. The software is intended primarily for minimizing objective functions that are nonconvex and/or nonsmooth. The package has implementations of two main algorithmic strategies: a gradient-sampling and a proximal-bundle method. Each algorithmic strategy can employ quasi-Newton techniques for accelerating convergence in practice. The … Read more

Sequential Rounding in Mixed-Integer Model Predictive Control

Categories Approximation Algorithms, Control Applications, Systems governed by Differential Equations Optimization Tags , , ,

This paper interfaces combinatorial integral approximation strategies with the inherent robustness properties of conventional model predictive control with stabilizing terminal conditions to establish practical asymptotic stability results for finite-control set and mixed-integer model predictive control. We examine the impact of sequential control rounding on the closed-loop performance in terms of stability and optimality. Sum-up rounding … Read more

The Least Singular Value Function in Variational Analysis

Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , , ,

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, met- ric regularity can be elusive for some important ill-posed classes of problems includ- ing polynomial equations, parametric variational systems, smooth reformulations of complementarity systems with degenerate solutions, etc. The study of stability issues for such … Read more

Optimal Control of Semilinear Graphon Systems

Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

We investigate optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. A graphon represents a limit object of a converging graph sequence and serves as a generalization of a finite graph, enabling a systematic analysis of large-scale networks. We analyze semilinear graphon dynamical systems and establish state convergence along … Read more

Obscured by terminology: Hidden parallels in direct methods for open-loop optimal control

Categories Control Applications, Scheduling, Systems governed by Differential Equations Optimization Tags , , , , ,

Active research on optimal control methods comprises the developments of research groups from various fields, including control, mathematics, and process systems engineering. Although there is a consensus on the classification of the main solution methods, different terms are often used for the same method. For example, solving optimal control problems with control discretization and embedded … Read more

Integer Control Approximations for Graphon Dynamical Systems

Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

Graphons generalize graphs and define a limit object of a converging graph sequence. The notion of graphons allows for a generic representation of coupled network dynamical systems. We are interested in approximating integer controls for graphon dynamical systems. To this end, we apply a decomposition approach comprised of a relaxation and a reconstruction step. We … Read more