Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond

Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

In this paper, the global optimization problem miny∈S F (y) with S being a hyperinterval in R and F (y) satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function F (y) can be multiextremal, non-differentiable, and given as a ‘black-box’. To attack the problem, a new global optimization algorithm based on the following two ideas is prop...

Global Nonlinear Parameter Estimation Using Interval Analysis: Parallel Computing Strategies

Dynamic optimization using adaptive control vector parameterization

In this paper we present a method for the optimization of dynamic systems using problem-adapted discretizations. The method is based on the direct sequential or single-shooting approach, where the optimization problem is converted into a nonlinear programming problem by parameterization of the control profiles. A fully adaptive, problem-dependent parameterization is generated by repetitive solu...

Fluid Injection Optimization Using Modified Global Dynamic Harmony Search

One of the mostly used enhanced oil recovery methods is the injection of water or gas under pressure to maintain or reverse the declining pressure in a reservoir. Several parameters should be optimized in a fluid injection process. The usual optimizing methods evaluate several scenarios to find the best solution. Since it is required to run the reservoir simulator hundreds of times, the process...

Global optimization of Lipschitz functions

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO wh...