Hikers in the Fog: Optimization Theory from Convex Bowls to Deep Networks

Deep End Era. Engineering with Sankalp · Oct 28, 2026 · 53m

Refinery engineer Benedikt Saari is training a soft sensor whose loss spikes and stalls, and his friend Lucía answers with five questions he cannot answer. In episode one hundred and twenty four we learn why each one matters. We walk landscapes as hikers in fog, discover why convex bowls are easy, meet Dantzig's simplex method, interior points and the KKT conditions whose Lagrange multipliers are a planner's shadow prices. Gradient descent zig-zags down badly conditioned canyons until normalisation turns them into bowls; reverse-mode differentiation gives a billion slopes for the price of…