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Equilibria of large random Lotka-Volterra systems with vanishing species: a mathematical approach
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix.
Complex systems in Ecology: a guided tour with large Lotka-Volterra models and random matrices
Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form $$ \frac{d x_i}{d t} = x_i \varphi_i(x_1,\cdots, x_N)\ , $$ where $N$ represents the number of species and $x_i$, the abundance of species $i$.
Stochastic Subgradient Descent Escapes Active Strict Saddles on Weakly Convex Functions
Consequently, generically in the class of definable weakly convex functions, the SGD converges to a local minimizer.
A Fully Stochastic Primal-Dual Algorithm
The proposed algorithm is proven to converge to a saddle point of the Lagrangian function.
A Constant Step Stochastic Douglas-Rachford Algorithm with Application to Non Separable Regularizations
The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions.
Snake: a Stochastic Proximal Gradient Algorithm for Regularized Problems over Large Graphs
When applying the proximal gradient algorithm to solve this problem, there exist quite affordable methods to implement the proximity operator (backward step) in the special case where the graph is a simple path without loops.
