Linear Programming: Foundations and Extensions

By Robert J. Vanderbei. 1998

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Citations in the corpus

Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks (2017, methodology): “the T R-satisability of conjunctions of linear atoms.2 Our algorithm extends simplex, and so we begin with an abstract calculus for the original algorithm (for a more thorough description see, e.g., [34]). The rules of the calculus operate over data structures we call congurations. For a given set o”
Sparse Recovery of Streaming Signals Using $\ell_1$-Homotopy (2013, background): “Starting from an available solution, a series of simple problems are solved along the so-called homotopy path towards the final solution of the original problem [24, 25, 47].”
Aggregation Functions: A Guide for Practitioners (2007, methodology): “, [59, 248]), and the solution to the dual problem allows one to recover that of the primal and vice versa.”
Computer poker: A review (2011, unknown): “One approach to determine these probability values is to represent the problem as an optimisation problem and use linear programming algorithms (such as the simplex algorithm [59] or interior point methods [93]) to derive a solution.”
An interior‐point algorithm for elastoplasticity (2007, unknown): “Thus, the paper of Karmarkar [41] in 1984 sparked a revolution which led to the development of the algorithms now known as interior-point methods [42–45].”
Adaptive computation and machine learning (1998, background): “1 is due to Vapnik and Chervonenkis (1971). We shall present a simplified version of the proof, as found in Devroye et al.”
Learning Entailment Relations by Global Graph Structure Optimization (2012, methodology): “In this article we tackle a similar problem of learning a transitive relation, but we use linear programming (Vanderbei 2008) to solve the optimization problem.”
Optimal design of a CMOS op-amp via geometric programming (2001, background): “, LANCELOT [16], MINOS [71], LOQO [97], or LINGO-NL [83].”
Introduction to dual composition for inference (2011, background): “This follows from strict complementary slackness (Vanderbei, 2007), which guarantees that a primal-dual pair (μ∗, δ∗) exists that satisfies the implication in (1.”
ROBUST BOUNDS FOR FORWARD START OPTIONS (2012, unknown): “Theorem 1 Suppose that call prices are given for a pair of maturities T 1 T 2 (for a continuum of strikes on each date) and that these prices are consistent with no-arbitrage 1 .”