Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced … Read more
The Mesh Adaptive Direct Search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features is a versatile search step in which quadratic models are built leading to a series of quadratically constrained quadratic subproblems. This work explores different algorithms that exploit the structure of the quadratic models: … Read more
We study the continuous newsvendor problem (i.e. a newsvendor problem concerning goods of a non-discrete nature, such as fresh fruit juice) and a class of stochastic dynamic programs with several application areas, such as inventory control of a continuous good, economics, and supply chain management. The class is characterized by continuous state and action spaces, … Read more
In this paper we analyze the rate of local convergence of the augmented Lagrange method for solving optimization problems with equality constraints and the objective function expressed as the sum of a convex function and a twice continuously differentiable function. The presence of the non-smoothness of the convex function in the objective requires extensive tools … Read more
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value when the stochastic program is expressed in terms of a law invariant coherent risk measure having a discrete Kusuoka representation. The obtained results … Read more
Locally weighted regression combines the advantages of polynomial regression and kernel smoothing. We present three ideas for appropriate and effective use of LOcally WEighted Scatterplot Smoothing (LOWESS) models for surrogate optimization. First, a method is proposed to reduce the computational cost of LOWESS models. Second, a local scaling coefficient is introduced to adapt LOWESS models … Read more
In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized … Read more
We describe trlib, a library that implements a Variant of Gould’s Generalized Lanczos method (Gould et al. in SIAM J. Opt. 9(2), 504–525, 1999) for solving the trust region problem. Our implementation has several distinct features that set it apart from preexisting ones. We implement both conjugate gradient (CG) and Lanczos iterations for assembly of … Read more
In this paper we deal with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy expenses. In a district the number of possible energy system combinations is really large, and a manual design approach might lead to a suboptimal solution. For this reason we designed a software … Read more
The quadratic shortest path problem (QSPP) is the problem of finding a path in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP known as the adjacent QSPP. It was … Read more