OR644 - Nonlinear Programming
Homeworks to date

• Homework 1, assigned Jan 23, due Jan 30 :
  • Prove the formulas for the gradient and Hessian of the quadratic function f(x)=1/2 xTQ x.  Here Q is a symmmetic matrix with elements q_ij
  • Determine the definiteness of the following matrices:
    • Q=[1 -2;-2 4] - (This notation indicates a matrix whose first row is (1,-2) and second row is (-2, 4))
    • Q=[0 -1 ;-1 0]
    • Q=[-1 -1 ;-1 -1]
    • Q=[4 -2 ;-2 1]
    • Q=[-1 2;2 -1]
    • Q=[-2 0 0; 0 -1 1; 0 1 -4]
  • Prove that if a symmetric matrix is positive definite, negative, or indefinite, its inverse is correspondingly, positive definite, negative definite, or indefinite. What can you say if the matrix is positive semidefinite?
  • Please read the Section on portfolio investment. Let me know of any comments ti you may have, typos you have found or any concerns you may have about readability
  • Suppose that x and y are both efficient portfolios. Would a strategy of investing half of your money in portfolio x and half of your money in portfolio y constitute an efficient portfolio?
• Homework 2, assigned Jan 30, due Feb 6:
  • Page 20 Problem 2,4
  • Page 24 Problems 1, 4, 10, 15
  • Page 32 Problems 1(a, b, c)
• Homework 3, assigned Feb 6 due Feb 13:
  • Page 36 (Section 2.6) problem 2(b)
  • Page 45 (Section 2.7) problem 1, 2(explain the reason for linear convergence in the first part).
  • Page 299 (Section 10.2) Problems 3, 4, 6, 7
• Homework 4, assigned Feb 20 due Feb 27:
  • Page 306 (Section 10.3), problems 1, 3, ,4
  • Page 311 (Section 10.4) problem 1 (You may use A=LL' rather than A=LDL')
  • Page 324 (Section 10.5) problem 1, 3
• Homework 5, assigned Feb 27 due Mar 6:
  • Page 344 (Section 11.2), problems 1, 2, 3, 5
  • Apply the Symmetric rank one method with an exact line search to problem 1 Page 341 problem 1
  • Page 356 (Section 11.3) Problems 1, 6.
  )
• Homework 6, assigned Mar 6 due Mar 20:
  • Page 389 (Section 12.2), problems 1, 2, 3
• Homework assigned Mar 27:
  • Review Sections 3.1, 3.2
• Homework 7, assigned Apr 3 due Apr 10:
  • Page 62 problems 1 (a),(b)
  • Page 434, problems 2, 5
  • Page 437 Problem 1
  • Page 445 problem 1
• Homework 8, assigned Apr 10 due Apr 17:
  • Page 453 problems 1 2, 4
• Project 2 links:
  wdbc.names
  wdbc.data
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