Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenious norm approach, when the number of points available does not allow to build a complete … Read more

Worst-case Complexity Bounds of Directional Direct-search Methods for Multiobjective Optimization

Direct Multisearch is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch takes … Read more

Trust-region methods without using derivatives: Worst case complexity and the non-smooth case

Trust-region methods are a broad class of methods for continuous optimization that found application in a variety of problems and contexts. In particular, they have been studied and applied for problems without using derivatives. The analysis of trust-region derivative-free methods has focused on global convergence, and they have been proved to generate a sequence of … Read more

Smoothing and Worst Case Complexity for Direct-Search Methods in Non-Smooth Optimization

For smooth objective functions it has been shown that the worst case cost of direct-search methods is of the same order as the one of steepest descent, when measured in number of iterations to achieve a certain threshold of stationarity. Motivated by the lack of such a result in the non-smooth case, we propose, analyze, … Read more