ffsshhttiikk 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