Optimization

Significant uncertainty and risk is associated with operation and maintenance costs for oil drilling. The requirement for service concepts is to guarantee high availability and productivity at low service costs during the service period. Failures of the oil rigs, the number of service technicians, the position of the home base and the availability of spare parts are the relevant parameters influencing the service costs. In addition various strategies combining scheduled and unscheduled maintenance can be considered.

We introduce a sparse time-frequency analysis method for analyzing nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently developed compressed sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions. We formulate this as a nonlinear optimization problem. Further, we propose an iterative algorithm to solve this nonlinear optimization problem recursively.

This lecture is based on the following papers: 1. A. Majda and B.
Gershgorin, 2010: Quantifying Uncertainty in Climate Change Science
Through Empirical Information Theory, PNAS in press 2. A. Majda, R.
Abramov, B. Gershgorin, High Skill in Low Frequency Climate Response
through Fluctuation Dissipation Theorems Despite Structural
Instability, PNAS, January 2010, Vol. 107, no. 2, pp 581 - 586. 3. B.
Gershgorin, A. Majda, Filtering A Nonlinear Slow-Fast System with

Optimization concepts will be reviewed with an eye on their proved or
potential application in Electronic Structure Calculations
and other Chemical Physics problems. We will discuss the role of
trust-region schemes, line searches, linearly and nonlinearly
constrained optimization, Inexact Restoration and SQP methods and the
type of convergence theories that may be useful in
order to explain the practical behavior of the methods. Emphasis will
be given on general principles instead of algorithmic details.