The optimal efficiency index of a class of Hermite iterative methods with two steps

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(Global) Optimization: Historical notes and recent developments

Recent developments in (Global) Optimization are surveyed in this paper. We collected and commented quite a large number of recent references which, in our opinion, well represent the vivacity, deepness, and width of scope of current computational approaches and theoretical results about nonconvex optimization problems. Before the presentation of the recent developments, which are subdivided into two parts related to heuristic and exact approaches, respectively, we briefly sketch the origin of the discipline and observe what, from the initial attempts, survived, what was not considered at all as well as a few approaches which have been recently rediscovered, mostly in connection with machine learning

Solving a class of generalized fractional programming problems using the feasibility of linear programs

Abstract This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm

An application of generalized fractional optmization in communications systems

Orientador: Paulo Augusto Valente FerreiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta dissertação aborda o problema de, dado um conjunto de razões de funções afins, maximizar o valor da menor das razões sobre uma região viável politópica. Para problemas nesta formulação, que generaliza a Otimização Linear-Fracionária e estende as suas aplicações em Matemática, Engenharia e Economia, existem de algoritmos de Otimização Global eficientes. Nesta dissertação estes algoritmos são revistos e aplicados a um problema específico de Alocação de Potência em Sistemas de Comunicação. Testes computacionais demonstram que os algoritmos propostos são mais eficientes do que os disponíveis atualmente na literatura para a aplicação consideradaAbstract: This dissertation considers the problem of, given a set of ratios of affine functions, maximizing the smallest ratio over a polytopic feasible region. For problems in this formulation, which generalizes the Linear-Fractional Optimization problem and extends its applications in Mathematics, Engineering and Economy, there exist efficient Global Optimization algorithms. In this dissertation these algorithms are reviewed and applied to a specific Power Allocation problem in Communication Systems. Computational tests show that the proposed algorithms are more efficient than the currently available in the literatura for the application consideredMestradoTelecomunicações e TelemáticaMestre em Engenharia Elétric