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24
Numerical solution of the stable, nonnegative definite Lyapunov equation
 IMA J. Numer. Anal
, 1982
"... We discuss the numerical solution of the Lyapunov equation ..."
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Cited by 88 (2 self)
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We discuss the numerical solution of the Lyapunov equation
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 75 (12 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.
Whiting \CDMA Data QoS Scheduling on the Forward Link with Variable Channel Conditions," Bell Laboratories
, 2000
"... ..."
Radioptimization  Goal Based Rendering
 In Computer Graphics Proceedings, Annual Conference Series
, 1993
"... This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the envir ..."
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Cited by 43 (0 self)
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This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the environment. The system solves for the "best" possible settings for: light source emissivities, element reflectivities, and spot light directionality parameters so that the design goals, suchastominimize energy or to give the the room an impression of privacy, are met. The system absorbs much of the burden for searching the design space allowing the user to focus on the goals of the illumination design rather than the intricate details of a complete lighting specification. A software implementation is described and some results of using the system are reported.
Optimal Utility Based MultiUser Throughput Allocation subject to Throughput Constraints
 Proceeding of INFOCOM'2005
"... ..."
Compact Representation of Images by Edge Adapted Multiscale Transforms
, 2001
"... We introduce new multiscale representations for images which incorporate a speci c geometric treatment of edges. The associated transforms are inherently nonlinear and non tensor product in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of comp ..."
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Cited by 29 (0 self)
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We introduce new multiscale representations for images which incorporate a speci c geometric treatment of edges. The associated transforms are inherently nonlinear and non tensor product in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of compression. This approach can be viewed as a bridge between edge detection and the nonlinear multiresolution representations of Ami Harten.
Computation of Minimum Volume Covering Ellipsoids
 Operations Research
, 2003
"... We present a practical algorithm for computing the minimum volume ndimensional ellipsoid that must contain m given points a 1 , . . . , am . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structur ..."
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Cited by 23 (0 self)
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We present a practical algorithm for computing the minimum volume ndimensional ellipsoid that must contain m given points a 1 , . . . , am . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interiorpoint methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interiorpoint and activeset method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30, 000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer.
Constrained gradient dynamic programming for stochastic optimal control of water resources systems, technical note
, 1986
"... A new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages. The algorithm, designated gradient dynamic programming, is a backward moving stagewise optimization. The main innovations over conventional di ..."
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Cited by 10 (2 self)
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A new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages. The algorithm, designated gradient dynamic programming, is a backward moving stagewise optimization. The main innovations over conventional discrete dynamic programming (DDP) are in the functional representation of the costtogo function and the solution of the singlestage problem. The costtogo function (assumed to be of requisite smoothness) is approximated within each element defined by the discretization scheme by the lowestorder polynomial which preserve its values and the values of its gradient with respect to the state variables at all nodes of the discretization grid. The improved accuracy of this Hermitian interpolation scheme reduces the effect of discretization error and allows the use of coarser grids which reduces the dimensionality of the problem. At each stage, the optimal control is determined on each node of the discretized state space using a constrained Newtontype optimization procedure which has quadratic rate of convergence. The set of constraints which act as equalities is determined from an active set strategy which converges under lenient convexity requirements. This method of solving the singlestage optimization is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence. Once the optimal control is determined, the costtogo function and its gradient with respect to the state variables is calculated to be used at the next stage. The proposed technique permits the efficient optimization of stochastic systems whose high dimensionality does not permit solution under the conventional DDP framework and for which successive approximation methods are not directly applicable due to stochasticity. Results for a fourreservoir example are presented. 1.
Modelling and Numerical Simulation of Martensitic Transformation in Shape Memory Alloys
, 2002
"... We consider the evolution of martensitic ne structures in shape memory alloys which undergo an isothermal phasetransformation. This process is modelled on a microscopical, continuummechanical level by partial differential equations. Here a homogeneous degree1 dissipation potential is involved whi ..."
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Cited by 9 (3 self)
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We consider the evolution of martensitic ne structures in shape memory alloys which undergo an isothermal phasetransformation. This process is modelled on a microscopical, continuummechanical level by partial differential equations. Here a homogeneous degree1 dissipation potential is involved which can reflect specific energies needed for rateindependent phase transformations. An interface energy is incorporated by a nonlocal term, and harddevice loading is considered. After setting up the model and specifying its energy balance properties, threedimensional numerical experiments for the cubictotetragonal transformation in an InTl single crystal are presented which demonstrate geometrical/material interactions under tensile and shear loading.
Algebraic Elimination of Slide Surface Constraints in Implicit Structural Analysis
, 2001
"... Slide surface and contact boundary conditions can be implemented via Lagrange multipliers in the algebraic equations in implicit structural analysis. This indefinite set of equations is di#cult to solve by iterative methods and is often too large to be solved by direct methods. When there are m cons ..."
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Cited by 2 (1 self)
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Slide surface and contact boundary conditions can be implemented via Lagrange multipliers in the algebraic equations in implicit structural analysis. This indefinite set of equations is di#cult to solve by iterative methods and is often too large to be solved by direct methods. When there are m constraints and there exists a set of m variables where each variable is only involved in a single constraint, we advocate a direct elimination technique which leaves a sparse, positive definite system to solve by iterative methods. We prove that the amount of "fillin" created by this process is independent of the size of the slide surfaces. In addition, the eigenvalues of the reduced matrix do not di#er significantly from the eigenvalues of the unconstrained matrix. This method can be extended to the case where constrained surfaces intersect and leads to a graph theoretic approach for determining which variables can be eliminated e#ciently for constraints with more general structure. 1