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Under the hypothesis that an initial point is a quasi-regular point, we use a majorant condition to present a new semi-local convergence analysis of an extension of the Gauss-Newton method for solving convex composite optimization problems. In this analysis the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where a Gauss-Newton sequence is "well behaved". AMSC: 47J15, 65H10.

The tick Rhipicephalus (Boophilus) microplus is a blood-sucking ectoparasite of cattle that severely impairs livestock production. Studies on tick immunological control address mostly single-antigen vaccines. However, from the commercial standpoint, so far no single-antigen vaccine has afforded appropriate protection against all R. microplus populations. In this context, multi-antigen cocktails have emerged as a way to enhance vaccine efficacy. In this work, a multi-antigenic vaccine against R. microplus was analyzed under field conditions in naturally infested cattle. The vaccine was composed by three tick recombinant proteins from two tick species that in previous single-vaccination reports provided partial protection of confined cattle against R. microplus infestations: vitellin-degrading cysteine endopeptidase (VTDCE) and boophilus yolk pro-cathepsin (BYC) from R. microplus, and glutathione S-transferase from Haemaphysalis longicornis (GST-Hl). Increased antibody levels against three proteins were recorded after immunizations, with a distinct humoral immune response dynamics for each protein. Compared to the control group, a statistically significant lower number of semi-engorged female ticks were observed in vaccinated cattle after two inoculations. This reduction persisted for 3 months, ranging from 35.3 to 61.6%. Furthermore, cattle body weight gain was significantly higher in vaccinated animals when compared to control cattle. Compared to the single-antigen vaccines composed by VTDCE, BYC or GST-Hl, this three-antigen vaccine afforded higher protection levels against R. microplus infestations.

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a b s t r a c tThe Gauss-Newton method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local convergence analysis is presented. This analysis allows us to obtain the optimal convergence radius and the biggest range for the uniqueness of stationary point, and to unify two previous and unrelated results.

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ADInternational audienceMultiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on “variational rationality” concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences