1,721,088 research outputs found
Analisi termodinamica e valutazione della sostenibilità ambientale di un sistema territoriale: lo studio della Provincia di Modena
No full textNumerical solution of a class of quasi-linear matrix equations
Full text linkGiven the matrix equation in the unknown matrix , we analyze existence and
uniqueness conditions, together with computational solution strategies for being a linear or nonlinear
function. We characterize different properties of the matrix equation and of
its solution, depending on the considered classes of functions . Our
analysis mainly concerns small dimensional problems, though several
considerations also apply to large scale matrix equations
Preconditioning of active-set Newton methods for PDE-Constrained optimal control problems
Full text linkWe address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We present two new preconditioners based on a full block matrix factorization of the Schur complement of the Jacobian matrices, where the active-set blocks are merged into the constraint blocks. We discuss the robustness of the new preconditioners with respect to the parameters of the continuous and discrete problems. Numerical experiments on 3D problems are presented, including comparisons with existing approaches based on preconditioned conjugate gradients in a nonstandard inner product
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion
Full text linkA new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. The convergence of the method is established. A prototype implementation is discussed and encouraging preliminary computational results are reported for solving the SDP-reformulation of matrix-completion problems
The Riemannian Barzilai-Borwein method with nonmonotone line search and the matrix geometric mean computation
Full text linkThe Barzilai-Borwein (BB) method, an effective gradient descent method with clever choice of the step length, is adapted from nonlinear optimization to Riemannian manifold optimization. More generally, global convergence of a nonmonotone line search strategy for Riemannian optimization algorithms is proved under some standard assumptions. By a set of numerical tests, the Riemannian BB method with nonmonotone line search is shown to be competitive in several Riemannian optimization problems. When used to compute the matrix geometric mean, known as the Karcher mean of positive definite matrices, it notably outperforms existing first-order optimization methods
Approximate norm descent methods for constrained nonlinear systems
Full text linkWe address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/ storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are "derivative-free" both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches
On the global convergence of a new spectral residual algorithm for nonlinear systems of equations
Full text linkWe present a derivative-free method for solving systems of nonlinear equations that belongs to the class of spectral residual methods. We will show that by endowing a previous version of the algorithm with a suitable new linesearch strategy, standard global convergence results can be attained under mild general assumptions. The robustness of the new method is therefore potentially improved with respect to the previous version as shown by the reported numerical experiments
A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
Full text linkWe propose an algorithm for computing the projection of a symmetric
second-order tensor onto the cone of negative semidefinite symmetric tensors
with respect to the inner product defined by an assigned positive definite
symmetric fourth-order tensor C. The projection problem is written as a
semidefinite programming problem and an algorithm based on a primal-dual
path-following interior point method coupled with a Mehrotra's
predictor-corrector approach is proposed. Implementations based on direct
methods are theoretically and numerically investigated taking into account
tensors C arising in the modelling of masonry-like materials
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