author = "Gouv{\^e}a, {\'E}rica Josiane Coelho and Regis, Rommel G. and 
                         Soterroni, Aline Cristina and Scarabello, Marluce da Cruz and 
                         Ramos, Fernando Manuel",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Saint 
                         Joseph’s University} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Instituto Nacional de Pesquisas Espaciais 
                         (INPE)} and {Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Global optimization using q-gradients",
              journal = "European Journal of Operational Research",
                 year = "2016",
               volume = "251",
               number = "3",
                pages = "727--738",
                month = "June",
             keywords = "Metaheuristics, Global optimization, q-calculus, q-gradient 
                         vector, Convergence.",
             abstract = "The q-gradient vector is a generalization of the gradient vector 
                         based on the q-derivative. We present two global optimization 
                         methods that do not require ordinary derivatives: a q-analog of 
                         the Steepest Descent method called the q-G method and a q-analog 
                         of the Conjugate Gradient method called the q-CG method. Both q-G 
                         and q-CG are reduced to their classical versions when q equals 1. 
                         These methods are implemented in such a way that the search 
                         process gradually shifts from global in the beginning to almost 
                         local search in the end. Moreover, Gaussian perturbations are used 
                         in some iterations to guarantee the convergence of the methods to 
                         the global minimum in a probabilistic sense. We compare q-G and 
                         q-CG with their classical versions and with other methods, 
                         including CMA-ES, a variant of Controlled Random Search, and an 
                         interior point method that uses finite-difference derivatives, on 
                         27 well-known test problems. In general, the q-G and q-CG methods 
                         are very promising and competitive, especially when applied to 
                  doi = "10.1016/j.ejor.2016.01.001",
                  url = "http://dx.doi.org/10.1016/j.ejor.2016.01.001",
                 issn = "0377-2217",
             language = "en",
           targetfile = "Gouvea_global.pdf",
        urlaccessdate = "04 dez. 2020"