Paolo Pugliese

Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints

In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem by the index scheme without introducing additional parameters or variables. A Branch-and-Bound method that does not use derivatives for solving the reduced problem is proposed. The method either determines the infeasibility of the original problem or finds lower and upper bounds for the global solution. Not all the constraints are evaluated during every iteration of the algorithm, providing a significant acceleration of the search. Convergence conditions of the new method are established. Extensive numerical experiments are presented.

Technical Communique: A global optimization technique for checking parametric robustness

This note investigates the possibilities offered by a novel global optimization technique in solving some minimization problems arising in Control Theory. The technique is described and some applications to typical control problems are reported.

Test Problems for Lipschitz Univariate Global Optimization with Multiextremal Constraints

In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. Two sets of test problems are introduced, in the first one both the objective function and constraints are differenliable functions and in the second one they are non-differentiable. Each series of tests contains 3 problems with one constraint, 4 problems with 2 constraints, 3 problems with 3 constraints, and one infeasible problem with 2 constraints. All the problems are shown in figures. Lipschitz constants and global solutions are given. For each problem it is indicated whether the optimum is located on the boundary or inside a feasible subregion and the number of disjoint feasible subregions is given. Results of numerical experiments executed with the introduced test problems using Pijavskii’s method combined with a non-differentiable penalty function are presented.

Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints

Abstract. Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a Hölder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.

Vandermonde matrices on integer nodes

Summary. This paper deals with Vandermonde matrices

Vandermonde matrices on integer nodes: the rectangular case

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A polynomial based SLAM algorithm for mobile robots using ultrasonic sensors - Experimental results

whose nodes are the first

P3P and P2P problems with known camera and object vertical directions

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Mobile robot localization in an unknown environment using sonar sensors and an incidence angle based sensors switching policy — Experimental results

integer numbers. We give an analytic factorization of such matrices and explicit formulas for the entries of their inverses, and explore their computational issues. We also give asymptotic estimates of the Frobenius norm of both

Maximizing performance and robustness of PI and PID controllers by global optimization

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