Results 1  10
of
18
Numerical solution of the stable, nonnegative definite Lyapunov equation
 IMA J. Numer. Anal
, 1982
"... We discuss the numerical solution of the Lyapunov equation ..."
Abstract

Cited by 87 (2 self)
 Add to MetaCart
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 descr ..."
Abstract

Cited by 75 (11 self)
 Add to MetaCart
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.
CDMA Data QoS Scheduling on the Forward Link with Variable Channel Conditions
, 2000
"... We consider the problem of scheduling CDMA data users on the forward link. The goal is to meet their QoS requirements defined in terms of probabilistic packet delay bounds. The constraint is the limit on the total forward link transmit power. Each user's channel condition is characterized by the ..."
Abstract

Cited by 59 (11 self)
 Add to MetaCart
We consider the problem of scheduling CDMA data users on the forward link. The goal is to meet their QoS requirements defined in terms of probabilistic packet delay bounds. The constraint is the limit on the total forward link transmit power. Each user's channel condition is characterized by the forward link power required to achieve a unit data rate. This paper extends the work reported in [1], in which several simplifying assumptions were made, including the assumption that channel conditions are constant in time. In this work, we study a more realistic scenario, in which transmission rates can only be chosen from a discrete finite set, rate scheduling can only be done at discrete scheduling intervals, and, most importantly, the users' channel conditions may vary in time.
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 ..."
Abstract

Cited by 42 (0 self)
 Add to MetaCart
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
 in Proceedings of IEEE INFOCOM ’05
, 2005
"... We consider the problem of scheduling multiple users sharing a timevarying wireless channel. (As an example, this is a model of scheduling in 3G wireless technologies, such as CDMA2000 3G1xEVDO downlink scheduling.) We introduce an algorithm which seeks to optimize a concave utility H i (R i ) o ..."
Abstract

Cited by 41 (10 self)
 Add to MetaCart
We consider the problem of scheduling multiple users sharing a timevarying wireless channel. (As an example, this is a model of scheduling in 3G wireless technologies, such as CDMA2000 3G1xEVDO downlink scheduling.) We introduce an algorithm which seeks to optimize a concave utility H i (R i ) of the user throughputs R i , subject to certain lower and upper throughput bounds: R i R i i . The algorithm, which we call the Gradient algorithm with Minimum/Maximum Rate constraints (GMR) uses a token counter mechanism, which modifies an algorithm solving the corresponding unconstrained problem, to produce the algorithm solving the problem with throughput constraints. Two important special cases of the utility functions are log R i and R i , corresponding to the common Proportional Fairness and Throughput Maximization objectives.
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 ..."
Abstract

Cited by 29 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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