Adrian Carrillo Galvez

Abstract
This work discusses and analyzes a class of nonconvex homogeneous optimization problems, in which the objective function is a positively homogeneous function with a certain degree, and the constraints set is determined by a single homogeneous function with another degree, and a geometric set which is a (not necessarily convex) closed cone. Once a Lagrangian dual problem is associated, it is provided various characterizations for the validity of strong duality property: one of them is related to the convexity of a certain image of the geometric set involving both homogeneous functions, so revealing a hidden convexity. We also derive a suitable S-lemma. In the case where both functions are of the same degree of homogeneity, a copositive reformulation of the original problem is established. It is also established zero-, first-and second-order optimality conditions; KKT (local or global) optimality, giving rise to the notion of L-eigenvalues with applications to symmetric tensors eigenvalues analysis.

Abstract

Abstract
Despite its worldwide relevance as an invasive plant, there are few studies on Ulex europaeus (gorse) and its allelopathic activity is almost unexplored. The allelochemical profile of gorse was analysed through methanolic extract of pods and roots, and its phytotoxic effects on Lactuca sativa germination. The methanolic extract of pods had no effect in germination, while extract of roots resulted in a U-shaped dose-response curve: reducing the germination at concentration 0.5 mg mL-1. GC-MS analysis detected compounds with proven antimicrobial and antioxidant activities in the pods and cytotoxic compounds in the roots, which could explain the bioassay results. The quinolizidine alkaloids (QAs) composition was evaluated to predict possible biological functions. It showed the presence of QAs in gorse that are absent in their native range, indicating broad defense strategies against bacteria, fungi, plants, and insects in the Chilean ecosystem. This could explain the superiority of gorse in the invaded areas.

Abstract
Although electricity is a clean and relatively safe form of energy when it is used, the generation and transmission of electricity have severe effects on the environment. An alternative to diminish the polluting emissions released by the generating units is the Emission Constrained Economic Dispatch (ECED). This is an optimization problem where the total fuel cost is minimized while treating emissions as a constraint with a pre-specified limit. Usually, the fuel cost and emission functions of the generating units must be experimentally derived, introducing then uncertainties in the obtained models. However, these uncertainties are often neglected and the ECED problem is solved considering the coefficients of the functions involved as exact (totally known) values. In this investigation we analyzed the effect of the uncertainties associated to the experimental derivation of the input–output curves of thermal power plants. Particularly, when polynomial models are fitted through multiple linear regression, we proposed an approach that, based on the respectively prediction intervals, can provide solutions immunized, in some sense, against variability in the coefficients estimates. We tested the proposed approach in a real system from the Chilean electrical power network. For the analyzed system we noted that, when uncertainties are not considered, the deterministic optimal solutions can be environmentally infeasible in some scenarios; whereas solutions obtained through the proposed approach, can significantly diminish the risk of environmental violations. The robustness of the prediction interval-based solutions was obtained with a negligible increase of the total fuel cost in all the cases studied.

Abstract
In this paper, Lagrangian dual formulation is used to solve the Environmental/Economic Dispatch problem. The proposed method, that results quite different from the metaheuristic methods employed in literature, was tested on a six generating units system. The results obtained improve others reported in previous investigations, by simultaneously diminishing the total fuel cost and pollutants emissions.