Notes
My notes (slides) during my PhD study in UMONS since Feb2017, email me if you catch a mistake/typo
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Tutorial/Lecture material
Continuous Optimization
General
Common glossaries in optimization
Linear Optimization
Coercive function
Projection operator is (firmly) nonexpansive and the obtuse angle criterion (BourbakiCheneyGoldstein inequality)
Proximal operator is nonexpansive and firmly nonexpansive
Augmented Objective Function  The introduction
Penalty and Barrier Method, Interior point method
Fenchel conjugate of norm is indicator function on unit ball of dual norm
Subdifferential of norm is \(\partial \ x \ = \left \{ v \in \mathbb{R}^n \Big  \langle v,x \rangle = \ x \, \ v \_* \leq 1 \right \}\)
Projection operator as proximal operator on indicator function
Project onto : nonnegative orthant, box and polyhedron, L2 ball, L1 ball, Lp ball, halfspace, simplex, nonnegative unimodal vector, cone, intersection of convex sets, \(L\)Lipschitz matrix
Nonnegative Matrix Factorizations : heuristics, algorithms, theory
Nonnegative Least Squares (NNLS) : algorithms
Theoretical aspects of Nonnegative Matrix Factorization
Nonnegative Matrix Factorization (NMF) : algorithms
Separable NMF
NMF in other norms
Matrix Completion
Theory
Algorithm
MC by MajorizationMinimization, by Proximal Point Algorithm / primaldual method, by Augmented Lagrangian Method, by DouglasRachford spitting algorithm, by ADMM, by Iterative Reweighted Least Squares
Linear Algebra / Matrix Theory
Randomized Linear Algebra, Compressive Sensing, Random Matrix
Multilinear/Tensor Algebra and Tensor methods
Algebra
Fundamentals of Tensor
Tensor shortcut : \(kr(U,V)^\top kr(U,V) = U^\top U \odot V^\top V\)
Canonical Polyadic Decomposition
The MTTKRP bottleneck
Tensor method (3rd order method) for optimisation
Theory
Machine Learning
On software engineering
