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Abstract. This paper presents a perturbation approach for performing sensitivity analysis of mathematical programming problems. Contrary to standard methods, the active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, Karush-Kuhn-Tucker multipliers, and objective function values may vary provided that optimality is maintained and the general structure of a feasible perturbation (which is a polyhedral cone) is obtained. This allows determining: (a) the local sensitivities, (b) whether or not partial derivatives exist, and (c) if the directional derivative for a given direction exists. A method for the simultaneous obtention of the sensitivities of the objective function optimal value and the primal and dual variable values with respect to data is given. Three examples illustrate the concepts presented and the proposed methodology. Finally, some relevant conclusions are drawn.

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Quinoa is a highly diverse crop domesticated in the Andean region of South America with broad adaptation to a wide range of marginal environments. Quinoa has garnered interest worldwide due to its nutritional and health benefits. Over the last decade, quinoa production has expanded outside of the Andean region, prompting multiple studies investigating the potential for quinoa cultivation in novel environments. Currently, quinoa is grown in countries spanning five continents, including North America, Europe, Asia, Africa, and Oceania. Here, we update the advances of quinoa research in Ecuador across different topics, including (a) current quinoa production situation with a focus on breeding progress, (b) traditional seed production, and (c) the impact of the work of the nongovernment organization “European Committee for Training and Agriculture” with quinoa farmers in Chimborazo province. Additionally, we discuss genetic diversity, primary pests and diseases, actions for adapting quinoa to tropical areas, and recent innovations in quinoa processing in Ecuador. Finally, we report a case study describing a participatory breeding project between Washington State University and the Association of Andean Seed and Nutritional Food Producers Mushuk Yuyay in the province of Cañar.