Optimal control problems including partial differential equation (PDE) as well integer constraints merge the combinatorial difficulties of programming and challenges related to large-scale systems resulting from discretized PDEs. So far, branch-and-bound framework has been most common solution strategy for such problems. In order provide an alternative approach, especially in a context, this ar...

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced o...

We present a class of adaptive multilevel trust-region methods for the efficient solution of optimization problems governed by time–dependent nonlinear partial differential equations with control constraints. The algorithm is based on the ideas of the adaptive multilevel inexact SQP-method from [26, 27]. It is in particular well suited for problems with time–dependent PDE constraints. Instead o...

In this work we introduce and perform a study on the multitime multi-objective fractional variational problem of minimizing a vector of quotients of path independent curvilinear integral functionals (MFP ) subject to certain partial differential equations (PDE) and/or partial differential inequations (PDI), using a geometrical language. The paper is organized as follows: §1 formulates a PDI&PDE...

The present paper deals with a class of second-order PDE constrained controlled optimization problems application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions optimality for the considered control driven by multiple integral cost functionals involving partial derivatives. Moreover, an illustrative example is provided to highlight effectiveness results d...

In this article, we describe an optimal control strategy for shaping a large-scale swarm of particles using boundary global actuation. This problem arises as key challenge in many robotics applications, especially when the robots are passive that need to be guided by external fields. The system is and underactuated, making at microscopic particle level infeasible. We consider Kolmogorov forward...

Parameter optimization problems constrained by partial differential equations (PDEs) appear in many science and engineering applications. Solving these optimization problems may require a prohibitively large number of computationally expensive PDE solves, especially if the dimension of the design space is large. It is therefore advantageous to replace expensive high-dimensional PDE solvers (e.g...