Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 16 May 2022 08:32:59 GMT2022-05-16T08:32:59Z10941Splitting methods for constrained quadratic programs in data analysishttp://hdl.handle.net/11380/304917Titolo: Splitting methods for constrained quadratic programs in data analysis
Abstract: This paper is concerned with the numerical solution of a linearly constrained quadratic programming problem by methods that use a splitting of the objective matrix. We present an acceleration step for a general splitting algorithm and we establish the convergence of the resulting accelerated scheme. We report the results of numerical experiments arising in constrained bivariate interpolation to evaluate the efficiency of this acceleration technique for a particular splitting of the objective matrix and for the corresponding extrapolated form.
Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/11380/3049171996-01-01T00:00:00ZA modified projection algorithm for large strictly-convex quadratic programshttp://hdl.handle.net/11380/304551Titolo: A modified projection algorithm for large strictly-convex quadratic programs
Abstract: In this paper, we propose a modified projection-type method for solving strictly-convex quadratic programs. This iterative scheme requires essentially the solution of an easy quadratic programming sub-problem and a matrix-vector multiplication at each iteration. The main feature of the method consists in updating the Hessian matrix of the subproblems by a convenient scaling parameter. The convergence of the scheme is obtained by introducing a correction formula for the solution of the subproblems and very weak conditions on the scaling parameter. A practical nonexpensive updating rule for the scaling parameter is suggested. The results of numerical experimentation enable this approach to be compared with some classical projection-type methods and its effectiveness as a solver of large and very sparse quadratic programs to be evaluated.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11380/3045512000-01-01T00:00:00ZSplitting methods and parallel solution of constrained quadratic programshttp://hdl.handle.net/11380/593955Titolo: Splitting methods and parallel solution of constrained quadratic programs
Abstract: In this work the numerical solution of linearly constrained quadratic programming problems is examined. This problem arises in many applications and it forms a basis for some algorithms that solve variational inequalities formulating equilibrium problems. An attractive iterative scheme for solving constrained quadratic programs when the matrix of the objective function is large and sparse consists in transforming, by a splitting of the objective matrix, the original problem into a sequence of subproblems easier to solve. At each iteration the subproblem is formulated as a linear complementarity problem that can be solved by methods suited for implementation on multiprocessor system. We analyse two parallel iterative solvers from the theoretical and practical point of view. Results of numerical experiments carried out on Cray T3D are reported.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/5939551997-01-01T00:00:00ZGPU acceleration of a model-based iterative method for Digital Breast Tomosynthesishttp://hdl.handle.net/11380/1199143Titolo: GPU acceleration of a model-based iterative method for Digital Breast Tomosynthesis
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11380/11991432020-01-01T00:00:00ZOn the Steplength Selection in Stochastic Gradient Methodshttp://hdl.handle.net/11380/1199144Titolo: On the Steplength Selection in Stochastic Gradient Methods
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11380/11991442020-01-01T00:00:00ZOn the stability of the direct elimination method for equality constrained least squares problemshttp://hdl.handle.net/11380/305507Titolo: On the stability of the direct elimination method for equality constrained least squares problems
Abstract: A backward error analysis of the direct elimination method for linear equality constrained least squares problems is presented. It is proved that the solution computed by the method is the exact solution of a perturbed problem and bounds for data perturbations are given. The numerical stability of the method is related to the way in which the constraints are used to eliminate variables and these theoretical conclusions are confirmed by a numerical example.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11380/3055072000-01-01T00:00:00ZIterative image reconstruction: a point of viewhttp://hdl.handle.net/11380/420984Titolo: Iterative image reconstruction: a point of view
Abstract: Several iterative methods are available for solving the ill-posed problem of image reconstruction. They are motivated by different approaches and may derive from methods used for the solutionof linear equations or the minimization of suitable functionals.In this paper we adopt the approach flowing from maximum likelihood to Bayesian formulation of image reconstruction and providing a generalization of the classical regularization theory. This approach leads to the minimization of functionals derived from properties of the noise and, possibly, from additional information on the solution.We investigate a class of scaled gradient methods, based on a suitable decomposition of the gradient, and we show that this class contains some of the methods used for the solution of maximum likelihood problems in image reconstruction. We also obtain very simple regularized versions of these methods. Constraints of non-negativity and flux conservation are taken into account by considering scaled gradient projection (SGP) methods, derived from the previous approach, and for them a convergence proof can be given. Numerical experience on a particular problem shows that SGP can provide a considerable increase in efficiency with respect to the standard algorithm used for that problem. Work is in progress in order to understand whether a similar gain can be achieved in other cases.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/4209842008-01-01T00:00:00ZNew adaptive stepsize selections in gradient methodshttp://hdl.handle.net/11380/421346Titolo: New adaptive stepsize selections in gradient methods
Abstract: This paper deals with gradient methods for minimizing n-dimensional strictly convex quadratic functions. Two new adaptive stepsize selection rules are presented and some key properties are proved. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the Barzilai-Borwein (BB) method, the cyclic/adaptive BB methods and two recent monotone gradient methods.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/4213462008-01-01T00:00:00ZSplitting and Projection-Type Methods for Large Convex Quadratic Programshttp://hdl.handle.net/11380/21018Titolo: Splitting and Projection-Type Methods for Large Convex Quadratic Programs
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11380/210182000-01-01T00:00:00ZTraining Support Vector Machines on Parallel Architectureshttp://hdl.handle.net/11380/21526Titolo: Training Support Vector Machines on Parallel Architectures
Abstract: The parallel solution of the large quadratic programming problem arising in training support vector machines is analysed. Some improvements to a recent decomposition technique are discussed. The effectiveness of the proposed approach is evaluated by solving large-scale benchmark problemson different parallel architectures.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/215262003-01-01T00:00:00Z