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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 descr ..."
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Cited by 74 (11 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.
Recent Advances in 2D and 2.5D Vortex statistics and dynamics
, 2005
"... This review paper offers both an overview of the recent developments in vortex statistics, and a detailed critical review of some of the advances as well as open problems in the area. A fruitful new direction in vortex dynamics concerns vortical systems with very large numbers of vortices in which s ..."
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Cited by 1 (1 self)
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This review paper offers both an overview of the recent developments in vortex statistics, and a detailed critical review of some of the advances as well as open problems in the area. A fruitful new direction in vortex dynamics concerns vortical systems with very large numbers of vortices in which statistical methods play a pivotal role. After a review of some of the older equilibrium statistical mechanics approaches, such as Onsagerâ€™s Vortex gas theory, we survey the recent burst of interest and papers on the application of statistical mechanics to a wide range of problems. They include many interesting problems such as rotating stratified flows with natural applications to atmospheric and oceanic sciences. Special models that will be discussed include point vortex as well as vortex blob models in axisymmetric flows, in the plane, and in geophysical flows involving multilayer baroclinic effects. A recent reverse application of a quantum pathintegral MonteCarlo algorithm to the LionsMajda model for nearly parallel vortex filaments will be reviewed with numerical results. A connection between these statistical theories and the classical numerical method known as the vortex method will also be made. Many of these noteworthy advances are made possible by good MonteCarlo algorithms, providing a crossdisciplinary aspect to the field. An important open problem in the field of the vortex gas is the exact partition function for any finite number of particles N and any finite temperature. 1.
SQ^P, Sequential Quadratic Constrained Quadratic Programming
, 1998
"... We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to find the next approximate minimizer. Asymptotically, finding the local minimizer ..."
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We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to find the next approximate minimizer. Asymptotically, finding the local minimizer of the quadratic model is equivalent to applying Newton's method to the stationarity condition. For constrained problems, the local quadratic model corresponds to minimizinga quadratic approximation of the objective subject to quadratic approximations of the constraints (Q 2 P), with an additional trust region. This quadratic model is intractable in general and is usually handled by using linear approximations of the constraints and modifying the Hessian of the objective using the Hessian of the Lagrangean, i.e. a SQP approach. Instead, we solve the Lagrangean relaxation of Q 2 P using semidefinite programming. We develop this framework and present an example which illustrates the adva...
Equilibrium Energy Density Spectrum for Two Dimensional Ows in the Zero Viscosity Limit and Random Matrices
"... This paper gives a microscopic derivation of the equilibrium energy density spectrum (per unit flow area) for the 2D Euler equations in a unbounded domain. The spectral density per unit flow area in the fundamental wavenumber interval q to q + 1 is given by E (q) = 16 3 K " dJ 1 (q + e(q)) q 2 # whe ..."
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This paper gives a microscopic derivation of the equilibrium energy density spectrum (per unit flow area) for the 2D Euler equations in a unbounded domain. The spectral density per unit flow area in the fundamental wavenumber interval q to q + 1 is given by E (q) = 16 3 K " dJ 1 (q + e(q)) q 2 # where scale factor 0 < d ! 1; and phase shift 0 < e(q) ! 0 as q !1: This derivation is based on a connection between the point vortex gas and the statistics of random matrices due to Wigner and Ginibre. N is the number of point vortices of strength in the calculation, and is taken to infinity in such a way that the total enstrophy K = N 2 is kept fixed. The particle density = N=A is also kept constant because the oneparticle reduced distribution function from random matrix theory implies that there is a effective radius L of the N vortex distribution, which scales like L N 1=2 : It is shown in this paper that the total kinetic energy per unit oflw area is finite and linear in the product K : E 0 = 1 X q=1 E (q) = 16 3 K 1 X q=1 " dJ 1 (q + e) q 2 # < 1: 1