Optimality conditions in convex multiobjective SIP

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P

Risk of infection in patients with lymphoma receiving rituximab: systematic review and meta-analysis

Background: The addition of Rituximab (R) to standard chemotherapy (C) has been reported to improve the end of treatment outcome in patients affected by CD-20 positive malignant lymphomas (CD20+ ML). Nevertheless, given the profound and prolonged immunosuppression produced by R there are concerns that severe infections may arise. A systematic review and meta-analysis were performed to determine whether or not the addition of R to C may increase the risk of severe infections in adults undergoing induction therapy for CD20+ ML.Methods: Only randomised controlled trials comparing R-C to C standard alone in adult patients with CD20+ ML were included. Meta-analysis was performed on overall incidence of severe infection, risk of dying as the consequence of infection, risk of febrile neutropenia, risk of severe leucopenia, risk of severe granulocytopenia and overall response assuming a fixed effect model. Heterogeneity was investigated, if present and I-2 >20%, according to several predefined baseline characteristics of the study populations.Results: Several relevant results have emerged. First, the addition of R to standard C does not increase the overall risk of severe infections (RR = 1.00; 95% CI 0.87 to 1.14) nor does it increase the risk of dying as a consequence of infection (RR = 1.60; 95% CI 0.68 to 3.75). Second, we confirmed that the addition of R to standard C increases the proportion of overall response (RR = 1.12; 95% CI 1.09 to 1.15), but it also increases the risk of severe leucopenia (RR = 1.24; 95% CI 1.12 to 1.37) and granulocytopenia (RR = 1.07; 95% CI 1.02 to 1.12).Conclusions: R-C is superior to standard C in terms of overall response and it does not increase the overall incidence of severe infection. However, data on special groups of patients (for example, HIV positive subjects and HBV carriers) are lacking. In our opinion more studies are needed to explore the potential effect of R on silent and chronic viral infections

Duality Mapping and Birkhoff Orthogonality

Abstract. In this note we establish some properties of Birkhoff orthogonality in terms of duality mapping. Particularly, using a slight extension of a Rockafellar result we obtain a new proof of a result earlier established by Blanco and Turnšek concerning the linear operators preserving Birkhoff orthogonality.</jats:p

Convexity and optimization in Banach spaces

Includes index and bibliographical referencesVanderbauwhede, André L