scholarly journals An interior-point $l_{\frac{1}{2}}$-penalty method for inequality constrained nonlinear optimization

2015 ◽  
Vol 12 (3) ◽  
pp. 949-973
Author(s):  
Kaiwen Meng ◽  
Xiaoqi Yang ◽  
Boshi Tian
Keyword(s):  
Nonlinear Optimization ◽  
Interior Point ◽  
Penalty Method ◽  
Constrained Nonlinear Optimization

scholarly journals Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

2014 ◽  
Vol 36 (3) ◽  
pp. A1251-A1276 ◽  
Author(s):  
Marcus J. Grote ◽  
Johannes Huber ◽  
Drosos Kourounis ◽  
Olaf Schenk
Keyword(s):  
Nonlinear Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Constrained Nonlinear Optimization

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

scholarly journals An interior-point trust-funnel algorithm for nonlinear optimization

2016 ◽  
Vol 161 (1-2) ◽  
pp. 73-134 ◽  
Author(s):  
Frank E. Curtis ◽  
Nicholas I. M. Gould ◽  
Daniel P. Robinson ◽  
Philippe L. Toint
Keyword(s):  
Nonlinear Optimization ◽  
Interior Point

Prediction of Performance and Design via Optimization of Ducted Propellers Subject to Non-axisymmetric Inflows

2005 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Hanseong Lee ◽  
Hua Gu ◽  
Yumin Deng
Keyword(s):  
Nonlinear Optimization ◽  
Pressure Coefficient ◽  
Optimization Method ◽  
Least Square ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Blade Design ◽  
Constrained Nonlinear Optimization ◽  
Nonlinear Optimization Method ◽  
Ducted Propellers

Recently developed methods at UT Austin for the analysis of open or ducted propellers are presented, and then coupled with a constrained nonlinear optimization method to design blades of open or ducted propellers for maximum efficiency satisfying the minimum pressure constraint for fully wetted case, or the specified maximum allowable cavity area for cavitating case. A vortex lattice method (named MPUF3A) is applied to analyze the unsteady cavitating performance of open or ducted propellers subject to non-axisymmetric inflows. A finite volume method based Euler solver (named GBFLOW) is applied to predict the flow field around the open or ducted propellers, coupled with MPUF-3A in order to determine the interaction of the propeller with the inflow (i.e. the effective wake) or with the duct. The blade design of open or ducted propeller is performed by using a constrained nonlinear optimization method (named CAVOPT-BASE), which uses a database of computed performance for a set of blade geometries constructed from a base-propeller. The performance is evaluated using MPUF-3A and GBFLOW. CAVOPT-BASE approximates the database using the least square method or the linear interpolation method, and generates the coefficients of polynomials based on the design parameters, such as pitch, chord, and camber. CAVOPT-BASE finally determines the optimum blade design parameters, so that the propeller produces the desired thrust for the given constraints on the pressure coefficient or the allowed amount of cavitation.

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