�� Professor Ellis Johnson
 31 May 2001 ~ 3 August 2001
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Thurs 31 May: Linear Programming           Quadratic Programming
          Models and Modeling Languages (AMPL, OPL, Concert)           Optimality Conditions and the Dual Problem
          Sparse Matrix Representation Thurs 12 July: Seperable Non-Linear Programming
          Primal-dual LP Using Least Squares           Non-Negative Least Squares problem
          The Revised Simplex Method           Primal LP Method Using Least Squares
          Crew Scheduling Problems           Bid Price Models in Revenue Management
Thurs 7 June: More Linear Programming Thurs 19 July: Integer Programming
          LP and IP Codes (CPLEX, Dash, OSL)           Strong LP Formulations and Preprocessing
          Steepest Edge Column Choice and Degeneracy           Clique Inequalities
          Inverting the Basis and Updating the Inverse           Covers and Lifting
          The Primal-Dual Simplex Algorithm           Coefficient Strengthening
Thurs 14 June: Lagrangian Methods and Decomposition           Probing and Bound Reduction
          The Lagrangian Function Thurs 26 July: Large-Scale Integer Programming
          The Subgradient Method           Symmetry and Column Generation
       Fleet Assignment, Aircraft Routing, 
          and Multi-Commodity Flows		           Dantzig-Wolfe Decomposition and IP
Thurs 28 June: Exact Lagrangian Methods           Column Generation and Branching
          Dual Ascent and Primal-Dual           Cutting Stock Problem and Knapsack Problem 
          Dantzig - Wolfe Decomposition Fri 3 August: Benders Decomposition
          Geometry of Dual Variables in Dantzig - Wolfe            Feasibility and Optimality Cuts
          Primal Dual Subproblem Method for 
          Crew Pairing Optimization		           Convergence
Thurs 5 July: Non-Linear Programming               Dual to Dantzig-Wolfe
          Separable Piece-wise Linear Convex Programming            Integer Variables and Non-Linear Functions
          Curve following and Convexification           Plant Location, Multi-Commodity Flows

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Note : The course will include use of modeling environments, commercial, LP codes, Matlab exercises, and airline examples
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Ellis Johnson is the Coca-Cola Chaired Professor in the School of Industrial and Systems Engineering. He received a B.A. in mathematics at Georgia Tech and a Ph.D. in operations research at the University of California. Before joining Georgia Tech in 1995, he was at IBM��s T.J. Watson Research Center for 26 years. There, he founded and managed the Optimization Center from 1982 until 1990, when he was named IBM Corporate Fellow. In 1980-1981, he was at the University of Bonn, Germany, as recipient of the Alexander Von Humboldt Senior Scientist Award. In 1984, he received the George Dantzig Award for his research in mathematical programming. In 1986, he was awarded the Lanchester Prize for his paper with Crowder and Padberg. In 1988, he was elected to the National Academy of Engineering. From 1990 to 1995, he began teaching and conducting research at Georgia Tech, where he co-founded and co-directed the Logistics Engineering Center with Professor George Nemhauser.