We consider the problem in which a fleet of unmanned aerial gliders is required to visit a number of locations and then land in one of the available landing sites while optimising some performance criteria, subject to operational constraints and flight dynamics. Such problems frequently occur in disaster mitigation, where fast aerial reconnaissance of points … Read more
The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more
We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more
This work addresses the structural compliance minimization problem through a level-set-based strategy that rests upon radial basis functions with compact support combined with Hilbertian velocity extensions. A consistent augmented Lagrangian scheme is adopted to handle the volume constraint. The linear elasticity model and the variational problem associated with the computation of the velocity field are … Read more
This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra … Read more
A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches … Read more
We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more
This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a … Read more
In this paper, we address the problem of maximizing the spectral gap of a divergence type diffusion operator. Our main application of interest is characterizing the distribution of a swarm of agents that evolve on a bounded domain in Rn according to a Markov process. A subclass of the divergence type operators that we introduce … Read more