Browsing by Author "Greenberg, Harvey J."
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- Convergence of Column Generation for Semi-infinite Programs in the Presence of Equality ConstraintsGreenberg, Harvey J. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1975)A convergence theorem is presented for the standard column generation algorithm which embodies GLM. The primary extension of earlier published theorems is the allowance of equality constraints. A related stability theorem is introduced to demonstrate robustness.
- An Exact Update for Harris' TreadGreenberg, Harvey J. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1975)The purpose of this note is to show how Harris' TREAD value can be computed without approximation.
- GLM Versus Continuous Approximation for Convex Integer ProgramsGreenberg, Harvey J. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1974)GLM is compared to continuous approximation for convex, integer programs. After noting the stronger bound provided by GLM, Lagrangian duality and a gap closing heuristic is used to demonstrate how GLM may provide a better feasible policy as well.
- On Computing a Buy/copy Policy Using the Pitt-Kraft ModelGreenberg, Harvey J.; Kraft, Donald H. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1975)The Pitt-Kraft model of buying versus photocopying results in a small, but complex, nonlinear program. This paper identifies a Kuhn-Tucker point and demonstrates that for certain parameter values it is not optimal. A policy generation procedure is presented; the purpose is to prevent convergence of a primal algorithm to this inferior policy, which satisfies the Kuhn-Tucker optimality conditions.
- Searching One Multiplier in GlmGreenberg, Harvey J. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1974)A unified approach is developed for one-dimensional GLM. The major result is a convergence theorem for interval reduction. Comparative analysis of bisection, linear interpolation and tangential approximation reveals the relative advantages of tangential approximation.