Homework for Week 6
Math 408 Section A, February 9
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Reading Assignment:
- Multivariable Calculus Review: Due Wednesday, January 28.
- Optimality Conditions for Unconstrained Problems: Due Monday, February 2.
- Optimality Conditions for Constrained Problems: Due Friday, February 6.
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Homework Assignment:
- Review for Midterm exam on Friday, February 13.
The midterm exam will be comprensive up to and including
the notes on Optimality conditions for Unconstrained Problems.
- Do all of the exercises in the notes on
unconstrained optimization.
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Vocabulary List:
- Optimality Conditions for Unconstrained Problems
- The directional derivative.
- The gradient and Hessian.
- Eigen-value decomposition for symmetric matrices.
- Positive definite and positive semi-definite matrices.
- First-order necessary conditions for optimality.
- Second-order necessary conditions for optimality.
- Second-order sufficient conditions for optimality.
- Convexity, sets and functions.
- Subdifferential inequality.
- Show that a local minimizer of a covex function
is a global minimizer.
- Necessary and sufficient conditions for optimality
in the convex case.
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Key Concepts:
- Eigen-values and eigen-vectors of symmetric matrices.
- Optimality Conditions
- Second-order Taylor expansion.
- Convexity
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Skills to Master:
- Checking optimality conditions
- Checking if a matrix is positive semi-definite
or positive semi-definite.
- checking convexity
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Midterm Exam:
-
The midterm exam will ahve 4 questions. One questions for each of
the following 4 areas:
- Present value and internal interest.
- Fixed income securities, especially bonds.
- Linear Programming.
- Unconstrained optimization and convexity.
See the
sample midterm exam
(PDF)
(PS).