# Variable substitution in optimisation: a paradox

Given an optimisation problem of the form $\min_{x,y} \{f(x,y) = g(x) + h(y), g(x) = \alpha y\}$, where $\alpha \neq 0$, can we equivalently solve the problem $\min_{x,y} \{\alpha y + h(y)\}$? Continue reading →

# Metric subregularity for monotone inclusions

Metric sub-regularity is a local property of set-valued operators which turns out to be a key enabler for linear convergence in several operator-based algorithms. However, conditions are often stated for the fixed-point residual operator and become rather difficult to verify in practice. In this post we state sufficient metric sub-regularity conditions for a monotone inclusion which are easier to verify and we focus on the preconditioned proximal point method (P3M). Continue reading →

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