Frequency of Offering: Every Third Semester

• Introduction to mathematical modeling
  General guidelines in model building; Basic steps in model formulation; The general form of a mathematical optimization model; Examples of mathematical models; Model validity.

• Linear programming
  Brief review of linear programming; Using a modeling language (e.g., LINGO, GAMS) to develop linear programming models; Solving linear programming problems using one or more of LINGO, LINDO, GAMS; Interpretation and analysis of results.

• Integer programming
  Formulating integer programming problems (such as knapsack problems, capital budgeting problems, sequencing problems, scheduling problems, set covering problems, and fixed charge problems); Graphical interpretation and solution of simple integer models; Basic concepts of branch-and-bound and implicit enumeration; Basic concepts of cutting-plane methods; Modeling and solution of integer programming problems using one or more of LINGO, LINDO, GAMS.

• Nonlinear programming
  Formulation of nonlinear programming problems (such as least-squares estimation, facility location models, portfolio selection, nonlinear transportation models); Numerical techniques for solving one-variable unconstrained problems (e.g., golden-section search, bisection search); Multivariate unconstrained optimization (e.g., Hooke-Jeeves, Newton's Method); Basic concepts of optimality conditions for constrained optimization and graphical interpretations; Modeling and solving general nonlinear programming problems using one or more of LINGO, GAMS.

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Last modified: February 26, 2007