Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Generalized Order-Value Optimization (GOVO) problems involve functions whose evaluation depends on order relations on some representation functional set. We give examples of GOVO problems that may be analyzed in the context of Piecewise-Smooth Optimization. Generalizations of algorithms that have been proved to be effective for proving special classes of GOVO problems are introduced. The case of Low Order-Value Optimization (LOVO) is considered as an example of GOVO in which one needs specialized algorithms with stronger convergence results. Applications of constrained LOVO problems and problems with OVO constraints are presented. The state-of-the-art of Protein Alignment problems from the LOVO point of view are discussed.201SI7598PRONEXFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAEP-UNICAMPFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [PT 2006-53768-0]