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LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is ..."
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Cited by 108 (21 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
QuasiNewton methods for unconstrained optimization
 J. Inst. Math. Appl
, 1972
"... Arevised algorithm is given for unconstrained optimization using quasiNewton methods. The method is based on recurring the factorization of an approximation to the Hessian matrix. Knowledge of this factorization allows greater flexibility when choosing the direction of search while minimizing the a ..."
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Cited by 64 (1 self)
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Arevised algorithm is given for unconstrained optimization using quasiNewton methods. The method is based on recurring the factorization of an approximation to the Hessian matrix. Knowledge of this factorization allows greater flexibility when choosing the direction of search while minimizing the adverse effects of rounding error. The control of rounding error is particularly important when analytical derivatives are unavailable, and a modification of the algorithm to accept finitedifference approximations to the derivatives is given. 1.
Optimal Parameters of a Sinusoidal Representation of Signals
, 1999
"... In the spectral analysis of digital signals, one of the most useful parametric models is the representation by a sum of phaseshifted sinusoids in form of P N 1 n=0 An sin(!n t + 'n ), where An , !n , and 'n are the component's amplitude, frequency and phase, respectively. This mode ..."
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Cited by 2 (2 self)
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In the spectral analysis of digital signals, one of the most useful parametric models is the representation by a sum of phaseshifted sinusoids in form of P N 1 n=0 An sin(!n t + 'n ), where An , !n , and 'n are the component's amplitude, frequency and phase, respectively. This model generally ts well speech and most musical signals due to the shape of the representation functions. If using all of the above parameters, a quite dicult optimization problem arises. The applied methods are generally based on eigenvalue decomposition [3]. However this procedure is computationally expensive and works only if the sinusoids and the residual signal are statistically uncorrelated. To speed up the representation process also rather ad hoc methods occur [4]. The presented algorithm applies the newly established Homogeneous Sinus Representation Function (HSRF) to nd the best representing subspace of xed dimension N by a BFGS optimization. The optimum parameters fA; !; 'g ensure the mean squar...
HESFCN  A FORTRAN Package of Hessian Subroutines for Testing Nonlinear Optimization Software
"... We report the development of Hessian FORTRAN routines for testing unconstrained nonlinear optimization. An existing package, "Algorithm 566" (J. Mor'e, B. G. Garbow, and K. Hillstrom, ACM Trans. Math. Softw. 7, 1441 and 136140, 1981) provides function and gradient subroutines of 1 ..."
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Cited by 1 (1 self)
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We report the development of Hessian FORTRAN routines for testing unconstrained nonlinear optimization. An existing package, "Algorithm 566" (J. Mor'e, B. G. Garbow, and K. Hillstrom, ACM Trans. Math. Softw. 7, 1441 and 136140, 1981) provides function and gradient subroutines of 18 test functions for multivariate minimization. Our supplementary Hessian segments will enable users to test optimization software that requires second derivative information. Eigenvalue analysis throughout the minimization will also be possible in the goal of better understanding minimization progress by different algorithms and the relation of progress to eigenvalue distribution and condition number. 1 Introduction A robust and easytouse package of FORTRAN subroutines for testing unconstrained optimization software was prepared about a decade ago [14,15]. The package includes testing software for three problem areas: systems of nonlinear functions, nonlinear least squares, and unconstrained minimiza...
Desktop Aeronautics, Inc.
, 2005
"... The purpose of this white paper is to provide a range of information to potential designers of oblique wing ..."
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The purpose of this white paper is to provide a range of information to potential designers of oblique wing
AN OPTIMIZATION BASED METHOD FOR DETERMINING EIGENPAIRS OF LARGE REAL MATRICES
"... Abstract. The determination of the eigenpairs of real matrices can be treated as a local optimization problem. Suitable nonnegative functions are constructed with coinciding local and global minima, which are located at the points defined by the eigenvectors of the underlying matrix. Some propertie ..."
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Abstract. The determination of the eigenpairs of real matrices can be treated as a local optimization problem. Suitable nonnegative functions are constructed with coinciding local and global minima, which are located at the points defined by the eigenvectors of the underlying matrix. Some properties of these eigenvector functions are investigated and proved. 1.