The phi-divergence proximal method is an extension of the proximal minimization algorithm, where the usual quadratic proximal term is substituted by a class of convex statistical distances, called phi-divergences. In ...
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The phi-divergence proximal method is an extension of the proximal minimization algorithm, where the usual quadratic proximal term is substituted by a class of convex statistical distances, called phi-divergences. In this paper, we study the convergence rate of this nonquadratic proximal method for convex and particularly linear programming. We identify a class of phi-divergences for which superlinear convergence is attained both for optimization problems with strongly convex objectives at the optimum and linear programming problems, when the regularization parameters tend to zero. We prove also that, with regularization parameters bounded away from zero, convergence is at least linear for a wider class of phi-divergences, when the method is applied to the same kinds of problems. We further analyze the associated class of augmented Lagrangian methods for convex programming with nonquadratic penalty terms, and prove convergence of the dual generated by these methods for linear programming problems under a weak nondegeneracy assumption.
In this paper identification of mixed parametric/nonparametric linear models is considered. A set membership setting is adopted. Disturbances are assumed to be bounded according to the 2-norm, while estimation errors ...
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In this paper identification of mixed parametric/nonparametric linear models is considered. A set membership setting is adopted. Disturbances are assumed to be bounded according to the 2-norm, while estimation errors are measured according to an H norm. Worst case optimal and suboptimal algorithms are analyzed, minimizing the H norm of the unstructured perturbation. The behavior of estimation errors for different model orders is discussed on application examples.
The Path Flow Estimator (PFE) is a software tool for estimating flows and travel times in transportation networks. It has been developed to support both on-line urban traffic management and off-line transportation pla...
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The Path Flow Estimator (PFE) is a software tool for estimating flows and travel times in transportation networks. It has been developed to support both on-line urban traffic management and off-line transportation planning. Given data from vehicle detectors and other forms of sensor, path flows and path travel times are inferred on the basis of a logit path choice model. The delays incurred by congestion are taken into account. The most significant paths in the network are generated by the iterative use of a shortest path algorithm, using link costs reduced by shadow prices incurred by active constraints (like traffic counts). In order to better represent the transitory overloads which characterise congested conditions, a time-dependent PFE has been formulated. Various versions of the PFE have been specified and are being validated for a number of European test sites.
This paper is devoted to the design of robust state feedback controllers for a class of linear uncertain systems. It is assumed that in the system and input matrices there are linear uncertain parameters, which satisf...
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This paper is devoted to the design of robust state feedback controllers for a class of linear uncertain systems. It is assumed that in the system and input matrices there are linear uncertain parameters, which satisfy no special restrictions, such as the matching condition or norm-bounded constraints. Through the matrix nonsingularity analysis, it is known that systems stabilized by a state feedback controller have robust stability bounds on the uncertain parameters, which can be computed from the structured singular value of a composite matrix. Based on this result and linear matrix inequalities, we form a convex optimization problem so that stabilizing controllers can be found to maximize the robust stability bounds.
The aim of this paper is to study the possibility to obtain efficient as well as satisfying solutions when solving a general non linear convex Goal programming problem. Firstly, uniqueness conditions are given under w...
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The aim of this paper is to study the possibility to obtain efficient as well as satisfying solutions when solving a general non linear convex Goal programming problem. Firstly, uniqueness conditions are given under which we can assure that the solution obtained is efficient. In case it is not efficient, some methods to obtain them are proposed, for both cases when there exist satisfying solutions for the problem, and when they do not exist In the first case, that is, when there exist satisfying solutions, an algorithm to approximate the set of solutions which are satisfying and efficient at the same time is given. Finally, some computational results are offered, showing the behaviour of the algorithm with several test problems.
In this paper, we study the global convergence of a large class of primal-dual interior point algorithms for solving the linearly constrained convex programming problem. The algorithms in this class decrease the value...
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In this paper, we study the global convergence of a large class of primal-dual interior point algorithms for solving the linearly constrained convex programming problem. The algorithms in this class decrease the value of a primal-dual potential function and hence belong to the class of so-called potential reduction algorithms. An inexact line search based on Armijo stepsize rule is used to compute the stepsize. The directions used by the algorithms are the same as the ones used in primal-dual path following and potential reduction algorithms and a very mild condition on the choice of the ''centering parameter'' is assumed. The algorithms always keep primal and dual feasibility and, in contrast to the polynomial potential reduction algorithms, they do not need to drive the value of the potential function towards - infinity in order to converge. One of the techniques used in the convergence analysis of these algorithms has its root in nonlinear unconstrained optimization theory.
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to constru...
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This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min-max stochastic queue location problem are reported.
A recurrent neural network, called a deterministic annealing neural network, is proposed for solving convex programming problems. The proposed deterministic annealing neural network is shown to be capable of generatin...
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A recurrent neural network, called a deterministic annealing neural network, is proposed for solving convex programming problems. The proposed deterministic annealing neural network is shown to be capable of generating optimal solutions to convex programming problems. The conditions for asymptotic stability, solution feasibility, and solution optimality are derived. The design methodology for determining design parameters is discussed. Three detailed illustrative examples are also presented to demonstrate the functional and operational characteristics of the deterministic annealing neural network in solving linear and quadratic programs.
In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algor...
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In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity, called the harmonic convexity in this paper. A characterization of this convexity condition is given. The same convexity condition was used by Mehrotra and Sun to prove the convergence of a path-following algorithm. The Iri-Imai algorithm is a natural generalization of the original Newton algorithm to constrained convex programming. Other known convergent interior-point algorithms for smooth convex programming are mainly based on the path-following approach.
We present a new method for minimizing a strictly convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions (thus the row-action nature ...
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We present a new method for minimizing a strictly convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions (thus the row-action nature of the algorithm) and at each iteration a subproblem is solved consisting of minimization of the objective function subject to one or two linear equations. Convergence of the algorithm is established and the method is compared with other row-action algorithms for several relevant particular cases.
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