Developing and Understanding Methods for Large Scale Nonlinear Optimization

2001 ◽  
Author(s):  
Robert B. Schnabel ◽  
Richard H. Byrd
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale

scholarly journals A Practical Algorithm for General Large Scale Nonlinear Optimization Problems

1999 ◽  
Vol 9 (3) ◽  
pp. 755-778 ◽  
Author(s):  
Paul T. Boggs ◽  
Anthony J. Kearsley ◽  
Jon W. Tolle
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Practical Algorithm

scholarly journals pyOptSparse: A Python framework for large-scale constrained nonlinear optimization of sparse systems

2020 ◽  
Vol 5 (54) ◽  
pp. 2564 ◽  
Author(s):  
Neil Wu ◽  
Gaetan Kenway ◽  
Charles Mader ◽  
John Jasa ◽  
Joaquim Martins
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Constrained Nonlinear Optimization ◽  
Sparse Systems

scholarly journals Numerical Performance of Different Formulations for Alternating Current Optimal Power Flow

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
Kibaek Kim
Keyword(s):  
Nonlinear Optimization ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Optimization Problems ◽  
Alternating Current ◽  
Box Constraints ◽  
Optimal Power ◽  
Wide Range ◽  
The Impact

<div>Alternating current optimal power flow (ACOPF) problems are nonconvex and nonlinear optimization problems. Utilities and independent service operators (ISO) require ACOPF to be solved in almost real time. Interior point methods (IPMs) are one of the powerful methods for solving large-scale nonlinear optimization problems and are a suitable approach for solving ACOPF with large-scale real-world transmission networks. Moreover, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. In this paper, different ACOPF formulations with various linear solvers and the impact of employing box constraints are evaluated for computational viability and best performance when using IPMs. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of sparsity. The numerical experiments suggest that the least sparse ACOPF formulations with polar voltages yield the best computational results. Additionally, nodal injected models and current-based branch flow models are improved by enforcing box constraints. A wide range of test cases, ranging from 500-bus systems to 9591-bus systems, are used to verify the test results.</div>

scholarly journals Decomposition of inseparable nonlinear optimization problems by the multilevel hierarchical method

2015 ◽  
Vol 1 (2) ◽  
pp. 1-6
Author(s):  
Nguyen Dinh Tai ◽  
Phan Dinh Dieu
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Descent Method ◽  
Dual Method ◽  
Hierarchical Method

For solving one class of nonlinear optimization problems of a large-scale stationary nonseparable system, composing N interacting subsystems has proposed a three-level algorithm based on a combination of the component descent method with the dual method. An approximate variant of this algorithm is established and the convergence of last under certain conditions is proved.

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