Optimal

Several numerical techniques will be presented for solving
discretized partial differential equations (PDEs) by special multilevel
methods based on one or no grid with nearly optimal computational
complexity in a user-friendly fashion.

A fundamental difficulty in stochastic optimization is the fact that
decisions may not be able pin down the values of future costs, but
rather can only, within limits, shape their distributions as random variables.
An upper bound on a ramdom cost is often impossible, or too expensive, to
enforce with certainty, and so some compromise attitude must be taken to
the violations that might occur. Similarly, there is no instant
interpretation of what it might mean to minimize a random cost, apart

Day 2: Using ideas from fluid dynamics, we derive a partial differential equation (pde) whose asymptotic solution solves the optimal transport problem in L2. Numerical schemes are then described allowing one to implement the pde on computer to be used in real-world applications.

Day 1: We introduce the Monge-Kantorovich (MK) problem and then give a brief overview of the calculus of variations, and how this may be used to treat Monge-Kantorovich, that is, the Optimal Transport problem.

I will give an overview of some recent mathematical results in the field of approximate Transformation Optics. The physical models discussed will range from the (single frequency) Helmholtz Equation to the full (non-local) Wave Equation. Time permitting I will also discuss optimization of approximate cloaks and the associated improved invisibility.

Soil structure is the arrangement of soil particles into secondary units called aggregates or peds. These manifest the cumulative effect of local pedogenic processes and influence soil behaviour - especially as it pertains to aeration and hydrophysical properties. One of the most direct methods of probing and characterizing soil structure is the analysis of the spatial arrangement of pore and solid spaces on images of sections of resin-impregnated soil or non-disruptive CT scanning.

In this talk we consider the modeling and control of building systems represented as large and complex systems. First, we present a motivation for why we believe a centralized approach to optimal operation may not be the best approach. Then, we present an approach for clustering building zones so as to create a decentralized architecture that balances achievable performance with tolerance to sensor/actuator faults. Here, performance is measured by temperature regulation.

Solving inverse problems for nonlinear simulation models with nonlinear objective is usually a global optimization problem. This talk will present an overview of the development of algorithms that employ response surfaces as a surrogate for an expensive simulation model to significantly reduce the computational effort required to solve continuous global optimization problems and uncertainty analysis of simulation models that require a substantial amount of CPU time for each simulation.

If a mathematical program (be it linear or nonlinear) has many symmetric optima, solving it via Branch-and-Bound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for: (a) automatically finding the formulation group of any given Mixed-Integer Nonlinear Program, and (b) reformulating the problem so that it has fewer symmetric solutions.