optimization

## What I do - Solve linear and nonlinear programming problems - Apply gradient descent and Newton methods - Work with constrained optimization (Lagrange multipliers) - Analyze convex optimization problems - Apply dynamic programming - Use integer and combinatorial optimization ## When to use me When maximizing/minimizing functions subject to constraints. ## Key Concepts - **Linear Programming**: Minimize c^Tx subject to Ax ≤ b, x ≥ 0 - **Gradient Descent**: x_{k+1} = x_k - α∇f for unconstrained minimization - **Lagrange Multipliers**: ∇f = λ∇g for constraint g(x) = 0 - **KKT Conditions**: Necessary conditions for constrained optima - **Convexity**: f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) ensures global optima - **Dynamic Programming**: Optimal substructure + memoization