Nonlinear Programming—Sequential Unconstrained Minimization Techniques

By M. Powell. 1969

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Citations in the corpus

Robots that can adapt like animals (2014, background): “The Squared Exponential covariance function and the Matérn kernel are the most common kernels for Gaussian processes 33,34,21 .”
An improved particle swarm optimizer for mechanical design optimization problems (2004, background): “[41] is that the static penalty coefficient rg requires to be fine tuned in order to generate an acceptable result.”
Second Order Optimality Conditions and Their Role in PDE Control (2015, methodology): “We will not address the associated second order conditions of the Karush-KuhnTucker theory and refer the reader to the textbooks [40, 61, 71].”
A Feature Selection Newton Method for Support Vector Machine Classification (2004, background): “The asymptotic exterior penalty problem [5, 1] for this linear program is the following nonnegatively constrained minimization problem:”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, methodology): “Davies and Swann [84], in connection with applying the pattern search method of Hooke and Jeeves to constrained optimization, recommend the use of the reciprocal barrier method of Carroll [54, 106].”
An interior‐point algorithm for elastoplasticity (2007, methodology): “The implicit methods, which have received by far the most attention, usually employ the backward-Euler scheme, e.g. Reference [1], for the local integration whereas Newton’s method is used for the global equilibrium iterations.”
Handbook of Semidefinite Programming (2000, background): “The fundamental idea of interiorpoint algorithms goes back at least to Frisch [271] and to Fiacco and McCormick [242].”
A general non‐linear optimization algorithm for lower bound limit analysis (2003, methodology): “Reference [10], and were later discovered to have a formal relationship with the modern interior point methods such as the celebrated method of Karmarkar.”
Implicit Functions and Solution Mappings (2009, unknown): “Theorem (Hildebrand–Graves). Let Q⊂ IRd and consider a function f : Q× IRn → IRn along with a point x̄ ∈ IRn. Suppose there are a positive constant a, a linear bounded mapping A : IRn → IRn which is invertible, and a positive constant M with M|A−1|< 1 such that (a) for all p ∈ Q and x,x′ ∈ IBa(x̄), ”
Asymptotics for lasso-type estimators (2000, unknown): “EEectively, we are using an unconstrained optimization problem (minimizing h in (22) for small ) to approximate a constrained optimization problem (minimizing h 0 in (23)); this is a standard trick in optimization (Fiacco and McCormick, 1990).”
Interior point methods 25 years later (2012, methodology): “(Interestingly, the use of a logarithmic barrier method in the context of optimization had already been proposed in 1955 by Frisch [37] and studied extensively by Fiacco and McCormick [32] in the context of nonlinear optimization.)”
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization (2005, methodology): “Our next convergence result is in the spirit of the sequential unconstrained minimization technique (SUMT) employed in [FM68].”
Shift-share analysis: further examination of models for the description of economic change (2000, background): “where l and l 0 are unconstrained dual variables [38].”