Optimization Theory and Methods: Nonlinear Programming

By Wenyu Sun, Ya-Xiang Yuan. 2010

1,013 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/790d90a2664ab94f87074f61a7d03334298530ac

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Citations in the corpus

Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM (2013, methodology): “We can write the NLP problem in a system of fractional differential equations as follows: Consider the unconstrained optimization problem (5), an approach based on fractional dynamic system can be described by the following FDEs Dα x(t) =−∇xF(x,µ), 0 α ≤ 1, (6) with the initial conditionsx(t0) =…”
Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets (2018, methodology): “Moreover, at best, these methods converge to the minimum at a rate of O 1 t 2 (Sun and Yuan 2006).”
Two optimal Dai–Liao conjugate gradient methods (2015, methodology): “In an attempt to suggest an extension of βHS k based on the standard secant equation,[3] Dai and Liao [4] (DL) dealt with the extended conjugacy condition dT k+1 yk = −tgT k+1sk which leads to the following CG parameter: βDL k = βHS k − t gT k+1sk dT k yk , (1.”
Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization (2016, unknown): “, [35, 43]).”
A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations (2019, unknown): “70)) of [49] det (I + u1u 2 + u3u 4 ) = (1 + uT 1 u2)(1 + uT 3 u4) − (uT 1 u4)(u 2 u3), (36)”
Generic Model of Active Distribution Network for Large Power System Stability Studies (2013, methodology): “The Levenberg-Marquardt algorithm [32] (available in Matlab System Identification Toolbox) that minimizes the sum of the squares of the vertical distances between data points and the fitted curve was used for parameter estimation as it is both fast and effective.”
Rayleigh Quotient Based Optimization Methods For Eigenvalue Problems (2014, methodology): “In the 1960s, it was extended by Fletcher and Reeves [11, 1964] as an iterative method for solving nonlinear optimization problems (see also [35, 48]).”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, methodology): “For the problemmin fθ(x), the TRM [140] uses the secondorder Taylor expansion to approximate the objective function fθ(x), denoted as qt(s).”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, background): “, [25, 39, 46]) is also discussed in [40] for low-rank matrix recovery problem based on this UV -parametrization.”