Optimization Course Assignments

Under supervision of Dr. Maryam Amirmazlaghani

< Homework one >

• Solve optimization problem using cvxpy library
• Minimize Quadratic Functions

< Homework two >

Unconstrained optimization algorithms

• Line Search methods

  • Find a decent direction
    • Steepest Decent
    • Newton
    • BFGS (a Quasi-Newton method)
  • Find a step length that satisfies wolfe conditions
    • Backtracking Line Search

• Trust Region methods

  • Construct a model function as ƒk + pT∇ƒk + 0.5 pTBkp by choosing a matrix as B_k
    • Hessian Matrix
  • Solve the constrained subproblem and find a step
    • Cauchy Point
    • Dogleg

< Homework three >

Unconstrained optimization algorithms
Solving large linear systems of equations: Ax = b or minx 0.5 xTAx - bTx

• Linear Conjugate Gradient

Constrained optimization algorithms
Solving inequality constrained minimization: minx 0.5 xTAx - bTx s.t. Px ≼ q

• Log Barrier
  • Solving an equality constrained minimization using Newton method on each iteration
• Primal Dual Interior Point