PDF Publication Title:
Text from PDF Page: 190
7.5 Hybrid Filter Trust-region Algorithm Finally, the performance of the algorithm depends significantly on the quality of the reduced-order model constructed. Highly accurate ROMs with sufficiently accurate gradients can quickly approach close to the optimum within Section I itself. On the other hand, ROMs which poorly predict the actual dynamic behavior and portray inaccurate gradients can end up landing in Section II quite early during optimization, making the whole process computation- ally demanding. Moreover, size of the trust-region and as a result, total number of iterations also rely significantly on ROM accuracy. POD-based ROMs can be made more accurate by adding more basis functions. However, it can also lead to ill-conditioned ROMs due to addition of those basis functions which do not affect the dynamics much. Hence, ROM-construction is the most important part of this algorithm. 7.5.9 Convergence and Optimality Section II of the Algorithm II is essentially the SQP-filter algorithm proposed by Fletcher et al. [72]. Therefore, if we make the following assumptions (AD) The sequence of iterates {xk} produced by Algorithm II lies within a closed, bounded domain Ω. (AR) If {xki } is any subsequence of iterates for which limi→∞ θki = 0, then a normal step vki exists for i sufficiently large, and ∥vki ∥ ≤ κv θki for some κv > 0. the following convergence property holds. Theorem 7.5.1. (See Theorem 15.5.13 in [54]) Suppose that (AF1)–(AF3), (A1)–(A4), (AD), and (AR) hold and the fraction of Cauchy decrease (FCD) condition χ RRk f (x +v )−f (x +s )≥κχ min ,∆ (7.43) kkkkkkfkβk k is satisfied for some κf > 0, and a bounded sequence of βk > 1. Then either the restoration procedure terminates unsuccessfully by converging to an infeasible first-order critical point of the normal subproblem (7.36), or there is a subsequence {kj} for which Chapter 7. Trust-region Framework for ROM-based Optimization 176PDF 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)