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David G. Luenberger
Researcher at Stanford University
Publications - 15
Citations - 5334
David G. Luenberger is an academic researcher from Stanford University. The author has contributed to research in topics: Linear programming & Penalty method. The author has an hindex of 5, co-authored 15 publications receiving 5315 citations.
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Linear and nonlinear programming
David G. Luenberger,Yinyu Ye +1 more
TL;DR: Strodiot and Zentralblatt as discussed by the authors introduced the concept of unconstrained optimization, which is a generalization of linear programming, and showed that it is possible to obtain convergence properties for both standard and accelerated steepest descent methods.
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Linear and Nonlinear Programming
David G. Luenberger,Yinyu Ye +1 more
TL;DR: Strodiot and Zentralblatt as mentioned in this paper introduced the concept of unconstrained optimization, which is a generalization of linear programming, and showed that it is possible to obtain convergence properties for both standard and accelerated steepest descent methods.
Book ChapterDOI
Conic Linear Programming
David G. Luenberger,Yinyu Ye +1 more
TL;DR: Although CLP has long been known to be convex optimization problems, no efficient solution algorithm was known until about two decades ago, when it was discovered that interior-point algorithms for LP can be adapted to solve certain CLPs with both theoretical and practical efficiency.
Book ChapterDOI
Basic Properties of Linear Programs
David G. Luenberger,Yinyu Ye +1 more
TL;DR: A linear program (LP) is an optimization problem in which the objective function is linear in the unknowns and the constraints consist of linear equalities and linear inequalities as discussed by the authors, and the exact form of these constraints may differ from one problem to another, but as shown below, any linear program can be transformed into the following standard form:
Book ChapterDOI
Penalty and Barrier Methods
David G. Luenberger,Yinyu Ye +1 more
TL;DR: For a problem with n variables and m constraints, penalty and barrier methods work directly in the n-dimensional space of variables, as compared to primal methods that work in (n − m)-dimensional space.