PDF Publication Title:
Text from PDF Page: 150
optimum, they assume first-order consistency conditions to be true. One of their major contri- butions is the introduction of scaled (or corrected) objective functions and constraints in the trust-region subproblem to enforce these consistency conditions. Later, Fahl [65] developed the TRPOD algorithm based on the Alexandrov’s approach with few modifications. In TRPOD, they relax the consistency conditions and use an inexact gradient based formulation suggested by Carter [41]. Moreover, they solve the trust-region subproblem approximately and utilize Toint’s algorithm [186] for step computation. However, Alexandrov’s correction for objective functions and constraints is essentially a part of the TRPOD. Bergmann et al. [25] also ap- plied the TRPOD algorithm for optimal control of the circular cylinder wake flow considered in the laminar regime. Kragel [112] developed a streamline diffusion POD methodology to construct ROMs which are tuned to a high-order Navier-Stokes solver, and applied a recursive multilevel trust-region algorithm [87, 88] for an optimal flow control problem. For optimal design problems, Weickum et al. [198] developed extended ROMs for the whole design space and developed a simple trust region strategy for globalization. The focus of all the aforementioned studies is only unconstrained optimization, and the strategies developed do not involve any discussion about the techniques to manage equality and inequality constraints. We demonstrated in section 6.5.4.2 that attaining feasibility in the ROM-based optimization problem cannot guarantee feasibility for the original optimiza- tion problem, and thus a systematic formulation to ensure feasibilty is desired. Eldred et al. [63] briefly discuss few ways to handle infeasibility in a trust-region based methodology for optimization problems involving ROMs, but do not provide any systematic rigorous frame- work. Alexandrov et al. extended their previous work on unconstrained optimization with approximate models, and included equality and inequality constraints as well in the original optimization problem [4, 5, 6, 7, 9, 10]. In particular, they develop three distinct algorithms for constrained optimization problems involving ROMs; Augmented Lagrangian AMMO based on an augmented Lagrangian formulation, MAESTRO-AMMO which involves an l2 penalty function as a merit function, and SQP-AMMO which utilizes an exact l1 penalty function as 7.1 Introduction Chapter 7. Trust-region Framework for ROM-based Optimization 136PDF Image | Design and Operation of Pressure Swing Adsorption Processes
PDF Search Title:
Design and Operation of Pressure Swing Adsorption ProcessesOriginal File Name Searched:
anshul_thesis.pdfDIY PDF Search: Google It | Yahoo | Bing
CO2 Organic Rankine Cycle Experimenter Platform The supercritical CO2 phase change system is both a heat pump and organic rankine cycle which can be used for those purposes and as a supercritical extractor for advanced subcritical and supercritical extraction technology. Uses include producing nanoparticles, precious metal CO2 extraction, lithium battery recycling, and other applications... More Info
Heat Pumps CO2 ORC Heat Pump System Platform More Info
CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com (Standard Web Page)