Titlebook: Large Scale Linear and Integer Optimization: A Unified Approach; Richard Kipp Martin Book 1999 Springer Science+Business Media New York 19

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Linear and Integer Linear Optimizationa unified manner and then demonstrate how to use this theory to solve very large real world problems. No prior knowledge of these topics is assumed, although this text is written for a mathematically mature audience. Our target audience is upper level undergraduate students and graduate students in

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Linear Systems and Inverse Projectionsed primarily on Dantzig and Eaves [109] and Williams [453]. Replacing constraints with variables is illustrated next in Section 3.2. We refer to the process of replacing constraints with variables as .. This is logical because in projection we replace variables with constraints. In Section 3.2 we a

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More on Simplex this chapter we continue with several enhancements to the basic algorithm and related issues. In Section 6.2 we continue the development of sensitivity analysis which was first discussed in Chapters 2 and 3. We show that an analysis of the simplex tableau provides dual variable values, reduced cost

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Interior Point Algorithms: Barrier Methods” of the polytope instead of on the boundary. This allowed a large step in the direction of a projected gradient. Another “centering” philosophy used to keep a solution from being “too close” to the boundary has its roots in the barrier methods of nonlinear programming. See Frisch [161] and Fiacco a

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Integer Programminghe decision variables represent discrete choices such as funding a project or not, opening a warehouse or not, etc. When some of the variables in a linear optimization problem are continuous and some are discrete the corresponding optimization problem is called a .. When all of the variables are req

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Projection: Benders’ Decompositionts of variables . ∈ ?{sun1} and y ∈ ?{sun2}. In particular, assume that the . matrix has very special structure so the problem in the . variables only, is a relatively “easy” problem. For example, if the y variables are fixed at y = y, . ≥ . — By might be the constraint set for a transportation prob

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