MATH 480  Linear & Nonlinear Programming (303)
Assignments #6 
Syllabus
Formulation
of linear programs. Basic
properties of linear programs. The
simplex method. Duality. Necessary and sufficient conditions for unconstrained
problems. Minimization of convex
functions. A method of solving unconstrained problems.
Equality and inequality constrained optimization.
The Lagrange multipliers theorem. The
KuhnTucker conditions. A method of
solving constrained problems.
Prerequisite:
Math
280; ICS 101, ICS 102, or ICS 103
Objectives
Textbook: Linear and Nonlinear Programming by E.G. Luenberger, 2^{nd} edition (1994).
Grading
Policy:
Week # 
Sections 
Topics 
1 
2.12.3 
Introduction, Examples of Linear Programming
Problems, Basic Solutions 
2 
2.42.5 
The Fundamental Theorem of Linear Programming,
Relations to Convexity 
3 
3.13.5 
Pivots, Adjacent Extreme Points, Determining a
Minimum Feasible Solution, Computational Procedure~Simplex Method,
Artificial Variables 
4 
3.73.8 
Matrix Form of the Simplex Method, The Revised
Simplex Method 
5 
4.14.2 
Dual Linear Programs, The Duality Theorem 
6 
4.34.5 
Relations to the Simplex Procedure, Sensitivity
and Complementary Slackness, The Dual Simplex Method 
7 
5.15.4 
Transportation Problem 
8 
6.16.4 
First Order Necessary Conditions, Examples of
Unconstarined Problems, SecondOrder Conditions, Convex and Concave
Functions, 
9 
6.5, 7.8 
Minimization and Maximization of Convex
Functions, Newton’s Method 
10 
9.19.4 
Modified Newton’s Method, Construction of the
Inverse, DavidonFletcherPowell Method, The Broyden Family 
11 
10.110.3 
Constraints, Tangent Plane, FirstOrder Necessary
Conditions 
12 


13 
10.510.6, 10.8 
SecondOrder Conditions, Eigenvalues in Tangent
Subspace, Inequality Constraints 
14 
12.112.3 
Penalty Methods, Barrier Methods,
Properties of Penalty and Barrier_Functions 
15 
14.114.2,14.4 
Quadratic
Programming, Direct Methods, Modified Newton’s Methods 