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In this article, we consider the case where the multicriteria programming problem is linear. Characterizing the set of efficient solutions by some constraint of 'reverse convex' type in the space of criteria, we formulate the problem of minimizing a function $f$ over the efficient set as a global optimization problem with a special structure. For the resulting problem, a decomposition branch and bound based algorithm is then proposed, in which the branching procedure is performed in the criteria space. Convergence properties of the algorithm are discussed, and preliminary computational results are reported.

In this paper, we investigate a backward problem for a fractional abstract evolution equation for which we wants to extract the initial distribution from the observation data provided along the final time $t = T.$ This problem is well-known to be ill-posed due to the rapid decay of the forward process. We consider a final value problem for fractional evolution process with respect to time. For this ill-posed problem, we construct two regularized solutions using quasi-reversibility method and quasi-boundary value method. The well-posedness of the regularized solutions as well as the convergence property is analyzed. The advantage of the proposed methods is that the regularized solution is given analytically and therefore is easy to be implemented. A numerical example is presented to show the validity of the proposed methods.

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