KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
Department of Mathematical
SYLLABUS (101) (Semester I, 20012002)
(Dr. Suliman AlHomidan)
Course # Math 480
Title Linear and Nonlinear Programming
Prerequisite Math 280, ICS 101 or ICS 102
Textbook Linear and Nonlinear Programming by E.G. Luenberger, 2^{nd} edition (1994).
Objectives
The course deals with the basic ideas of mathematical programming (linear and nonlinear). We shall see how simple mathematics plays a significant role in the development of these ideas. The students will be asked to work out the computational implementation of a numerical algorithm for solving Linear and Nonlinear Programming problems and do presentations.
Current Catalogue Description
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 inequahit)’ constrained optimization. The Lagrange multipliers. The KuhnTucker conditions. A method of solving constrained problems.
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, 7.6, 7.8 
Minimization and Maximization of Convex Functions, The Method of Steepest Descent, 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 