Numerical Optimization: Theoretical and Practical Aspects

By J. Bonnans, Jean Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal. 2003

1,054 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Discrete Mathematics and Combinatorics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ac64188a839714f458a105e4608c3f2d9ec4318c

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In Control and Systems Engineering

In Discrete Mathematics and Combinatorics

In Management Science and Operations Research

Citations in the corpus

Prediction of surface roughness in extrusion-based additive manufacturing with machine learning (2019, methodology): “The optimal weights assigned to the base learners are determined using the sequential quadratic optimization (SQP) method [25].”
Consistency of trace norm minimization (2007, background): “(11) in order to make it differentiable, while controlling the increase of duality gap yielded by the added function (Bonnans et al., 2003).”
More efficiency in multiple kernel learning (2007, methodology): “Indeed, the output of the approximately solved SVM leads only to an ε-subgradient (Bonnans et al., 2003; Bach et al., 2004).”
DIFFRAC: a discriminative and flexible framework for clustering (2007, methodology): “More refined optimization schemes, based on smoothing of the spectral function J(B) by minM<0,trM=n,Φλ0 (M)>k[trBM +εtrM (2)] are also used to speed up convergence (steepest descent of a smoothed function is generally faster than subgradient iterations) [13].”
Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming (2006, methodology): “To guarantee this condition, is obtained based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [ 15 ], with Powell correction [25].”
On the Convergence of the Concave-Convex Procedure (2009, neutral): “See [2, Section 11.3] for details. minimization.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “ wt−1 and compute any minimizer wt∈ argmin w∈C max i∈{0,...,t−1} Ψ(wi) +Ψ′(wi)⊤(w−wi) . The main iteration of Kelley’s method (which can be seen in particular as an instance of a cutting-plane method [26]) thus requires to be able to solve a subproblem which may be complicated. When Cis a polytope, ”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, background): “An optimization problem with non isolated solutions is generally more difficult to solve than one with a unique solution [5].”
Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions (2008, methodology): “We propose to determine the root(s) τ of F by Newton’s method (see [14, 4] for instance).”
Almost Global Convergence to Global Minima for Gradient Descent in Deep Linear Networks (2018, background): “Indeed the step size can be chosen in terms of an a priori bound for the whole trajectory, which is explicitly determined only with the initial condition (see [4]).”
Self-concordant analysis for logistic regression (2009, neutral): “Finally, we let denote P and E general probability measures and expectations.”