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A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
TLDR
A new nonlinear conjugate gradient method and an associated implementation, based on an inexact line search, are proposed and analyzed and an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion is obtained.
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A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
TLDR
For the L-BFGS method and the unconstrained optimization problems in the CUTE library, the new nonmonotone line search algorithm used fewer function and gradient evaluations, on average, than either the monotone or the traditional nonMonotone scheme.
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A SURVEY OF NONLINEAR CONJUGATE GRADIENT METHODS
This paper reviews the development of dierent versions of nonlinear conjugate gradient methods, with special attention given to global convergence properties.
Runge-Kutta methods in optimal control and the transformed adjoint system
  • W. Hager
  • Computer Science
    Numerische Mathematik
  • 1 December 2000
TLDR
The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle to determine the convergence rate for Runge-Kutta discretizations of nonlinear control problems.
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Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems,…
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Joint transceiver design for MIMO communications using geometric mean decomposition
TLDR
This paper proposes a joint transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zero-forcing VBLAST decoder or the more recent dirty paper precoder, and proves that the scheme is asymptotically optimal for (moderately) high SNR in terms of both channel throughput and bit error rate (BER) performance.
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Updating the Inverse of a Matrix
TLDR
The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed.
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Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent
TLDR
This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.
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Lipschitz Continuity for Constrained Processes
  • W. Hager
  • Mathematics, Computer Science
  • 1 May 1979
TLDR
It is proved that the optimal control and the dual multipliers for strictly convex control problems with convex constraints on the state and the control are Lipschitz continuous in time.
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Uniform channel decomposition for MIMO communications
TLDR
A transceiver design that can decompose, in a strictly capacity lossless manner, a MIMO channel into multiple subchannels with identical capacities is proposed and it is shown that UCD can achieve the maximal diversity gain.
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