Numerical optimization by Jorge Nocedal

Where I and E are sets of indices, x are the variables and f is the objective function

Learning

When both the objective function and all the constraints are linear functions of x, the problem is a linear programming problem.

Linear programs are convex programs, and therefore all local solutions are global solutions.

Stochastic optimization optimize the expected performance of the model, for deterministic optimization problems the model is fully specified.

Convex programming :

• objective function is convex
• equality constraints are linear
• inequality constraints are concave