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.

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Featured Application The presented solution can be applied to simplify and hasten the development of gamified programming exercises conforming to the Framework for Gamified Programming Education (FGPE) standard.Abstract Skilled programmers are in high demand, and a critical obstacle to satisfying this demand is the difficulty of acquiring programming skills. This issue can be addressed with automated assessment, which gives fast feedback to students trying to code, and gamification, which motivates them to intensify their learning efforts. Although some collections of gamified programming exercises are available, producing new ones is very demanding. This paper presents GAMAI, an AI-powered exercise gamifier, enriching the Framework for Gamified Programming Education (FGPE) ecosystem. Leveraging large language models, GAMAI enables teachers to effortlessly apply storytelling to describe a gamified scenario, as GAMAI decorates natural language text with the sentences needed by OpenAI APIs to contextualize the prompt. Once a gamified scenario has been generated, GAMAI automatically produces exercise files in a FGPE-compatible format. According to the presented evaluation results, most gamified exercises generated with AI support were ready to be used, with no or minimum human effort, and were positively assessed by students. The usability of the software was also assessed as high by the users. Our research paves the way for a more efficient and interactive approach to programming education, leveraging the capabilities of advanced language models in conjunction with gamification principles.

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Software is developed using programming languages whose choice is made based on a wide range of criteria, but it should be noted that the programming language selected can affect the quality of the software product. In this paper, we focus on analysing the differences in energy consumption when running certain algorithms that have been developed using different programming languages. Therefore, we focus on the software quality from the perspective of greenability, in concrete in the aspects related to energy efficiency. For this purpose, this study has conducted an empirical investigation about the most suitable programming languages from an energy efficiency perspective using a hardware-based consumption measurement instrument that obtains real data about energy consumption. The study builds upon a previous study in which energy efficiency of PL were ranked using a software-based approach where the energy consumption is an estimation. As a result, no significant differences are obtained between two approaches, in terms of ranking the PL. However, if it is required to have a more realistic knowledge of consumption, it is necessary to use hardware approaches. Furthermore, the hardware approach provides information about the energy consumption of specific DUT hardware components, such as, HDD, graphics card, and processor, and a ranking for each of component is elaborated. This can provide useful information to make a more informed decision on the choice of a PL, depending on several factors, such as the type of algorithms to be implemented, or the effects on power consumption not only in overall, but also depending on specific DUT hardware components.