On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of solution maps to a class of parameterized generalized equations

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed

On the Aubin property of solution maps to parameterized variational systems with implicit constraints

In the paper, a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems, the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g. parameter-dependent quasi-variational inequalities and implicit complementarity problems. The result is based on a general condition ensuring the Aubin property of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative. Our final condition can be verified, however, without an explicit computation of these coderivatives. The procedure is illustrated by an example. © 2019, © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.The research of the first author was supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of the second author was supported by the Grant Agency of the Czech Republic, Project 17-04301S and the Australian Research Council, Project 10.13039/501100000923DP160100854

Improving the performance of a traffic system by fair rerouting of travelers

Some traffic management measures route drivers towards socially-desired paths in order to achieve the system optimum: the traffic state with minimum total travel time. In previous attempts, the behavioral response to route advice is often not accounted for since some drivers are advised to take significantly longer paths for the system’s benefit. Hence, these drivers may not comply with such advice and the optimal state will not be achieved. In this paper, we propose a social routing strategy to approach the optimal state while accounting for fairness in the resulting state. This routing strategy asks travelers to take a limited detour in order to improve efficiency. We show that the best possible paths (in terms of efficiency) to be proposed by a service adopting this strategy can be found by solving a bilevel optimization problem with a non-unique lower-level solution. We use techniques from parametric analysis to show that the directional derivative of the lower-level link flows however exists. This derivative is the optimal solution of a quadratic optimization problem with a suitable route flow solution as parameter. We use the derivative in a descent algorithm to solve the bilevel problem. Numerical experiments in a realistic environment show that the routing strategy only asks a small fraction of the drivers to take a limited detour and thereby substantially improves the performance of the traffic system

Necessary Conditions for Super Minimizers in Constrained Multiobjective Optimization

This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives