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
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
We investigate the local linear convergence properties of the Alternating Direction Method of Multipliers (ADMM) when applied to Semidefinite Programming (SDP). A longstanding belief suggests that ADMM is only capable of solving SDPs to moderate accuracy, primarily due to its sublinear worst-case complexity and empirical observations of slow convergence. We challenge this notion by introducing … Read more
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
Climate change is increasingly impacting power system operations, not only through more frequent extreme weather events but also through shifts in routine weather patterns. Factors such as increased temperatures, droughts, changing wind patterns, and solar irradiance shifts can impact both power system production and transmission and electric load. The current power system was not designed … Read more
Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more
Local error bounds play a fundamental role in mathematical programming and variational analysis. They are used e.g. as constraint qualifications in optimization, in developing calculus rules for generalized derivatives in nonsmooth and set-valued analysis, and they serve as a key ingredient in the design and convergence analysis of Newton-type methods for solving systems of possibly … Read more
Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca Mira and Miguel García (2017), and by the block-coordinate descent for single objective optimization problems, we present a decomposition theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements … Read more
In this paper, we address a challenging problem faced by a Brazilian oil and gas company regarding the rescheduling of helicopter flights from an onshore airport to maritime units, crucial for transporting company employees. The problem arises due to unforeseen events like bad weather or mechanical failures, leading to delays or postponements in the original … Read more
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