### Optimization III: Stochastic, Constrained, and Penalized Optimization (Introduction to Statistical Computing)

Lecture
19: Stochastic, Constrained, and Penalized Optimization.

Constrained optimization: maximizing multinomial likelihood as an example of
why constraints matter. The method of Lagrange multipliers for equality
constraints. Lagrange multipliers as shadow prices, indicating how much a
marginal weakening of the constraint would improve the optimum. Inequality
constraints and their Lagrange multipliers. Mathematical programming. Barrier
methods for inequality constraints. The correspondence between constrained and
penalized optimization.

Stochastic optimization: Difficulties of optimizing statistical functions
when the data is large. Sampling as an alternative to averaging over the whole
data. Stochastic gradient descent and stochastic Newton's method as an
application of sampling. Simulated annealing to escape local minima.

Optional reading 1: Léon Bottou and Olivier Bosquet, "The Tradeoffs of Large Scale Learning"

Optional reading 2: Francis
Spufford, Red
Plenty
(cf.);
Herbert Simon, The Sciences of the Artificial, especially chapters
5 and 8.

Introduction to Statistical Computing

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