A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation

By M. Powell. 1994

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In Mathematical Optimization

Citations in the corpus

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions (2005, methodology): “Another class of methods are the derivative-free optimization methods by Powell (1994, 2000, 2002) and by Conn et al. (1997) which utilize multivariate polynomial interpolation models within a trust-region framework.”
Recent approaches to global optimization problems through Particle Swarm Optimization (2002, unknown): “However, these methods require the Hessian or the gradient, respectively, in contrast to other optimization procedures, like the Nonlinear Simplex method (Nelder and Mead, 1965), the direction set method of Powell (Fletcher, 1987), or some other recently proposed methods (Boutsinas and Vrahatis, 200”
UOBYQA: unconstrained optimization by quadratic approximation (2002, methodology): “The present work is a development of a method that uses linear polynomial models for constrained calculations (Powell, 1994).”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, methodology): “Powell [109] proposed to use a linear model of the objective within a trust-region method.”
Bi-level model reduction for coupled problems (2009, methodology): “In this work, a parameter-dependent POD is proposed to decompose the coupling variables (Bui-Thanh et al. 2003; Newman 1996 ).”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, methodology): “Powell [220] proposed using a simplex because of the fact that it contains the minimum number of points required to capture first-order effects.”
pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization (2011, unknown): “This optimizer is an implementation of Powell’s nonlinear derivative-free constrained optimization that uses a linear approximation approach (Powell 1994).”
On the Lagrange functions of quadratic models that are defined by interpolation* (2001, methodology): “Instead the present work began with some numerical testing of a method that uses linear polynomial models for constrained calculations (Powell, 1994).”
Action Sets: Weakly Supervised Action Segmentation Without Ordering Constraints (2017, methodology): “For minimization, we use constrained optimization by linear approximation (COBYLA) [23].”
Scalable Global Optimization via Local Bayesian Optimization (2019, methodology): “For example, the popular COBYLA [35] method approximates the objective function using a local linear model.”
A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning: Principals, Recent Advances, and Applications (2020, background): “For example, the off-the-shelf DFO solver COBYLA [15] only supports problems with a maximum of 2(16) variables (SciPy Python library [16]), which is smaller than the size of a single ImageNet image [17].”