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OR3300-5300, Cornell University, School of OR&IE ------------------------------------------------ This course is designed to be a rigorous introduction to linear programming and the simplex algorithm. The following topics are covered: - LP models and various applications economic significance of LP history of LP - linear systems, basic feasible solutions - solution via the simplex algorithm recognizing infeasibility (two-phase algorithm) and unboundedness implicit treatment of upper/lower bounds revised simplex algorithm, computation via basis inverse and reduced costs - duality theory economic motivation via pricing and two-person zero-sum games Farkas theorem, LP duality theorem, complementary slackness duality for general LP models interpretation of duality in algorithmic setting - sensitivity analysis simple model sensitivity for objective and right-hand side coefficients parametric programming for objective and right-hand side vectors
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Unformatted text preview: - dual simplex algorithm use in sensitivity analysis adding/deleting rows/columns in basic LP model with solution recovery via primal and dual algorithms- transportation problem graph interpretation (spanning trees) of basic solutions specialized algorithms for this model basis unimodularity and integrality of solutions sensitivity analysis and graphical interpretation- geometry of LP and related topics convexity, polyhedra, polytopes, extreme points, edges, rays correspondence: extreme points <--> basic feasible solutions geometric significance of the simplex algorithm degeneracy, cycling, proof of finite convergence using least-index rule for cycle avoidance- computational complexity Klee-Minty examples of exponential worst-case behavior of simplex alg. discussion of polynomial-time algs. for combinatorial problems *************************************************...
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