Direct Multisearch (DMS) is a Derivative-free Optimization class of algorithms suited for computing approximations to the complete Pareto front of a given Multiobjective Optimization problem. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with … Read more
In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well–known Nesterov’s accelerated gradient method. At each iteration of our scheme, the new point is computed by performing a line–search scheme using a search direction given by a linear … Read more
We consider degree-d forms on the Euclidean unit sphere. We specialize to our setting a genericity result by Nie obtained in a more general framework. We exhibit an homogeneous polynomial Res in the coefficients of f, such that if Res(f) is not zero then all points that satisfy first- and second-order necessary optimality conditions are … Read more
In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature. Here, we propose to modify one of these algorithms, namely ALGENCAN by Andreani et al., in such a way to incorporate … Read more
We describe and analyse a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth mapping over a polyhedral set, such formulation includes Karush-Kuhn-Tucker (KKT) systems, variational inequalities problems, and generalized Nash equilibrium problems. Our algorithm is based on a modification of the fast locally convergent Linear Programming (LP)-Newton method with a … Read more
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … Read more
Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely … Read more
The minimum sum-of-squares clustering problem (MSSC) consists in partitioning n observations into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose an exact algorithm for the MSSC problem based on the branch-and-bound technique. The lower bound is computed by … Read more
NOMAD is software for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic features published in scientific publications. These features are motivated by real applications encountered by industrial partners. The latest major release of NOMAD, version 3, dates from 2008. Minor releases are produced as new features … Read more
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for the Euclidean projection onto the feasible set defined by these two constraints, based on which a simple gradient … Read more