↗Optimization
Linear programming, nonlinear, convex optimization, dynamic programming
Subfields
Linear Programming
Simplex method, duality, sensitivity analysis
Nonlinear Optimization
Gradient descent, Newton's method, constrained optimization
Convex Optimization
Convex functions, KKT conditions, interior point methods, ML applications
Integer Programming
Branch and bound, cutting planes, mixed integer programming
Dynamic Programming
Bellman equation, memoization, algorithm applications
Concepts
Optimization Basics
Optimization is finding variable values that maximize or minimize an objective function under given constraints.
Gradient Descent
Gradient descent is an optimization algorithm that iteratively moves in the opposite direction of the gradient to find the minimum.
Lagrange Multipliers
Lagrange multipliers method solves optimization problems with equality constraints by combining constraints with new variables (multipliers).
Linear Programming
Linear programming optimizes a linear objective function under linear constraints. The simplex algorithm solves it efficiently.
Convex Optimization
Convex optimization minimizes a convex function over a convex set. Local minima are global minima, making it efficiently solvable.