This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the ` 1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program.

. A computational algorithm is proposed for image enhancement based on total variation minimization with constraints. This constrained minimization problem is introduced by Rudin et al [13, 14, 15] to enhance blurred and noisy images. Our computational algorithm solves the constrained minimization problem directly by adapting the affine scaling method for the unconstrained l 1 problem [3]. The resulting computational scheme, when viewed as an image enhancement process, has the feature that it can be used in an interactive manner in situations where knowledge of the noise level is either unavailable or unreliable. This computational algorithm can be implemented with a conjugate gradient method. It is further demonstrated that the iterative enhancement process is efficient. Key Words. image enhancement, image reconstruction, deconvolution, minimal total variation, affine scaling algorithm, projected gradient method Department of Computer Science and Advanced Computing Research Institut...

We study preconditioning strategies for linear systems with positive-definite matrices of the form Z T GZ, where Z is rectangular and G is symmetric but not necessarily positive definite. The preconditioning strategies are designed to be used in the context of a conjugate-gradient iteration, and are suitable within algorithms for constrained optimization problems. The techniques have other uses, however, and are applied here to a class of problems in the calculus of variations. Numerical tests are also included.

Very large and geometrically complex scenes, exceeding millions of polygons and hundreds of objects, arise naturally in many areas of interactive computer graphics. Time-critical rendering of such scenes requires the ability to trade visual quality with speed. Previous work has shown that this can be done by representing individual scene components as multiresolution triangle meshes, and performing at each frame a convex constrained optimization to choose the mesh resolutions that maximize image quality while meeting timing constraints. In this paper we demonstrate that the nonlinear optimization problem with linear constraints associated to a large class of quality estimation heuristics is efficiently solved using an active-set strategy. By exploiting the problem structure, Lagrange multipliers estimates and equality constrained problem solutions are computed in linear time. Results show that our algorithms and data structures provide low memory overhead, smooth levelof -detail contro...

Computer and communication systems are often subject to variabilities and uncertainties in workload. For example, device demands at a server in a client-server system may be different at different times of the day, or the service time in a transaction processing system may vary with the size of the database. Exact values for parameters may be unknown at early stages of software design but approximate ranges for these parameter values may be available. A conventional queueing network model used for evaluating the performance of computer and communication systems accepts single values as model inputs and computes a single value for each performance measure of interest. Existence of uncertainties or variabilities in service demands makes the use of a single mean value for each model parameter inappropriate causing the conventional modeling approach to become ineffective. This paper proposes to use histograms for characterizing one or more model parameters that are associated with such unc...

This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [9]. The step computation is performed in two stages. In the rst stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the `1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active atthesolution of the linear program. The EQP incorporates a trust-region constraint and is solved (inexactly) by means of a projected conjugate gradient method. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEr [1] test set.

. A nonlinearly constrained optimization problem can be solved by the exact penalty approach involving nondifferentiable functions P i jc i (x)j and P i max(0; c i (x)). In [11], a trust region affine scaling approach based on a 2-norm subproblem is proposed for solving a nonlinear l 1 problem. The (quadratic) approximation and the trust region subproblem are defined using affine scaling techniques. Explicit sufficient decrease conditions are proposed to obtain a limit point satisfying complementarity, dual feasibility, and second order optimality. In this paper, we present the global convergence properties of this new approach. Key Words. nonlinearly constrained minimization, trust region, sufficient decrease conditions, affine scaling, exact penalty, nonlinear l 1 problem, global convergence 1 Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-90ER25...

. We present an application of our time-critical multiresolution rendering algorithm to the visual and possibly collaborative exploration of large digital mock-ups. Our technique relies upon a scene description in which objects are represented as multiresolution meshes. We perform a constrained optimization at each frame to choose the resolution of each potentially visible object that generates the best quality image while meeting timing constraints. We present numerical and pictorial results of the experiments performed that support our claim that we can maintain a fixed frame-rate even when rendering very large datasets on low-end graphics PCs. 1 Introduction When undertaking a large and long-time lasting engineering or architectural project, it is vital to verify quite often what could be the consequences of the decisions taken during the design phase. Nowadays this is usually done by crafting physical mock-ups, typically made of wood or plaster, that help the designers t...

In this book, I attempt to reach two goals. The first is purely mathematical: to clarify some of the basic concepts of probability theory. The second goal is physical: to clarify the methods to be used when handling the information brought by measurements, in order to understand how accurate are the inferences they allow. Probability theory is solidly based on Kolmogorov axioms, but the basic inference tool provided by Kolmogorov’s theory is the definition of conditional probability. While some simple problems can be solved though this notion of conditional probability, more elaborate problems, in particular, most of the inference problems that use inaccurate observations require a more advanced probability theory. When considering sets, there are some well known notions, for instance, the intersection of two sets, or, when a mapping is considered between two sets, the notion of image of a set, or of reciprocal image of a set. I develop in this book the theory that generalizes these notions when, instead of sets,

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