In solving a robust version of regularized least-squares with weighting, a certain scalar-valued optimization problem is required in order to determine the regularized robust solution and the corresponding robustified weighting parameters. This letter establishes that the required optimization problem does not have local, non-global minima over the interval of interest. This property is proved ...

The Minima Hopping global optimization method uses physically realizable molecular dynamics moves in combination with an energy feedback that guarantees the escape from any potential energy funnel. For the purpose of finding reaction pathways, we argue that Minima Hopping is particularly suitable as a guide through the potential energy landscape and as a generator for pairs of minima that can b...

This paper describes a new technique for generating convex, strictly concave and indeenite (bilinear or not) quadratic programming problems. These problems have a number of properties that make them useful for test purposes. For example, strictly concave quadratic problems with their global maximum in the interior of the feasible domain and with an exponential number of local minima with distin...

This paper improves constrained simulated annealing (CSA), a discrete global minimization algorithm with asymptotic convergence to discrete constrained global minima with probability one. The algorithm is based on the necessary and suucient conditions for discrete constrained local minima in the theory of discrete La-grange multipliers. We extend CSA to solve nonlinear continuous constrained op...

Using the Matrix-Tree Theorem and coupling methods the convergence of the Parallel Chain (PC) algorithm to the set of global minima is established for various selection functions. It is illustrated that there may be convergence to a set of non-global minima when selecting one of the best states (Best-Wins strategy). In the latter case the convergence of the homogeneous PC algorithm is proved fo...

Learning new representations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced, called induced regularized factor mo...