119,880 research outputs found
Introduction to Methods for Nonlinear Optimization
No full textThis book has two main objectives:
• to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level;
• to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research.
The basic material on unconstrained and constrained optimization is organized into two blocks of chapters:
• basic theory and optimality conditions
• unconstrained and constrained algorithms.
These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses.
A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems.
In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems.
The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course
A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations
No full textPresentazione della XIII edizione del rapporto della Società Geografica Italiana “Per una geopolitica delle migrazioni. Nuove letture dell’altrove tra noi” (Roma, 22 ottobre 2018)
No full textl 22 ottobre 2018, nella Sala della Regina presso la Camera dei Deputati
a Palazzo Montecitorio, è stato presentato il XIII Rapporto della Società
Geografica Italiana dal titolo Per una geopolitica delle migrazioni. Nuove letture dell’altrove tra noi. Come evidenziato da Ernesto Mazzetti, già Vicepresidente
della SGI, che ha coordinato i lavori, il XIII Rapporto si pone in continuità
con il primo Rapporto della SGI dal titolo L’altrove tra noi. Dati, analisi e valutazioni sul fenomeno migratorio in Italia, pubblicato nel 2003. Un’operazione tesa
quindi a ribadire sia l’interesse verso il fenomeno migratorio, di grande attualità oggi come nel 2003, sia a esprimere la volontà di riprendere la pubblicazione regolare del Rapporto. Quasi un ritorno alle origini, quando la SGI, con
l’allora Presidente Franco Salvatori, decise di dare avvio alla pubblicazione
con l’intento di approfondire il tema in ottica geografica e dare un contributo
alla lettura critica di quel tema, auspicando con ciò di contribuire all’orientamento dei processi decisionali della politica
An unconstrained minimization method for solving low rank SDP relaxations of the max cut problem
No full textIn this paper we consider low-rank semidefinite programming (LRSDP)
relaxations of combinatorial quadratic problems that are equivalent to the maxcut
problem. Using the Gramian representation of a positive semidefinite matrix, the
LRSDP problem can be formulated as the nonconvex nonlinear programming prob-
lem of minimizing a quadratic function with quadratic equality constraints. For the
solution of this problem we propose a continuously differentiable exact merit func-
tion that exploits the special structure of the constraints and we use this function to
define an efficient and globally convergent algorithm. Finally, we test our code on an
extended set of instances of the maxcut problem and we report comparisons with other
existing codes
Nonmonotone derivative-free methods for nonlinear equations
No full textIn this paper we study nonmonotone globalization techniques, in connection with iterative derivative-free methods for solving a system of nonlinear equations in several variables. First we define and analyze a class of nonmonotone derivative-free linesearch techniques for unconstrained minimization of differentiable functions. Then we introduce a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone linesearches, and we study the application of this scheme to some recent extensions of the Barzilai-Borwein gradient method and to hybrid stabilization algorithms employing linesearches along coordinate directions. Numerical results on a set of standard test problems show that the proposed techniques can be of value in the solution of large-dimensional systems of equations
Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems
No full textIn this paper we consider the standard linear SDP problem, and its low rank
nonlinear programming reformulation, based on a Gramian representation of a positive semi-
definite matrix. For this nonconvex quadratic problem with quadratic equality constraints,
we give necessary and sufficient conditions of global optimality expressed in terms of the
Lagrangian function
Decomposition Techniques for Multilayer Perceptron Training
No full textIn this paper, we consider the learning problem of multilayer perceptrons (MLPs) formulated as the problem of minimizing a smooth error function. As well known, the learning problem of MLPs can be a difficult nonlinear nonconvex optimization problem. Typical difficulties can be the presence of extensive flat regions and steep sided valleys in the error surface, and the possible large number of training data and of free network parameters. We define a wide class of batch learning algorithms for MLP, based on the use of block decomposition techniques in the minimization of the error function. The learning problem is decomposed into a sequence of smaller and structured minimization problems in order to advantageously exploit the structure of the objective function. Theoretical convergence results are established, and a specific algorithm is constructed and evaluated through an extensive numerical experimentation. The comparisons with the state-of-the-art learning algorithms show the effectiveness of the proposed techniques
Stopping Criteria for Linesearch Methods without Derivatives
No full textIn this paper acceptability criteria for the linesearch stepsize are introduced which require only function values. Simple algorithm models based on these criteria are presented. Some modifications of criteria based on the knowledge of the directional derivative are also illustrated
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
No full textWe give new convergence results for the block Gauss–Seidel method for problems where the feasible set is the Cartesian product of m closed convex sets, under the assumption that the sequence generated by the method has limit points. We show that the method is globally convergent for m=2 and that for m>2 convergence can be established both when the objective function f is componentwise strictly quasiconvex with respect to m−2 components and when f is pseudoconvex. Finally, we consider a proximal point modification of the method and we state convergence results without any convexity assumption on the objective functio
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