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In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of m decisions makers make joint decisions sequentially, which we refer to as mbm optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an mbm optimization algorithm converges to the team-optimum. As a second contribution, we present a local and greedy algorithm characterized by approximate decision strategies (i.e., strategies based on a local state vector) that return the same decisions as in the complete information framework (where strategies are based on full state vector). As a last contribution, we also show that there exists a subclass of submodular team problems, recognizable in polynomial time, for which the pbp optimization converges for at least an opportune initialization of the algorithm. [ABSTRACT FROM AUTHOR]

The paper proposes a general theory for the treatment of a class of optimization problems that arise as a consequence of a search for the optimal replenishment schedule for finite time horizon inventory models. The decision variables in these optimization problems consist of the number of replenishment periods and the lengths of the periods. When the number of replenishment periods is fixed, it is shown that the optimization problems have a unique solution under some partial differential inequalities. Furthermore, the minimal value is convex as a function of the number of replenishment periods. This leads to a simple procedure for determining the optimal control policy. [ABSTRACT FROM AUTHOR]

The goal of this paper is to give a rigorous justification for the Hessian-constrained problems introduced in [G. Bouchitté and I. Fragal`a, Arch. Ration. Mech. Anal., 184 (2007), pp. 257-284] and to show how they are linked to the optimal design of thin plates. To that aim, we study the asymptotic behavior of a sequence of optimal elastic compliance problems in the double limit when both the maximal height of the design region and the total volume of the material tend to zero. In the vanishing volume limit, a sequence of linear constrained first order vector problems is obtained, which in turn-in the vanishing thickness limit-produces a new linear constrained problem where both first and second order gradients appear. When the load is orthogonal to the plate, only the Hessian constraint is active, and we recover as a particular case the optimization problem studied in [G. Bouchitté and I. Fragal`a, Arch. Ration. Mech. Anal., 184 (2007), pp. 257-284] (see also [T. Lewinski and J. J. Telega, Arch. Mech. (Arch. Mech. Stos.), 53 (2001), pp. 457-485]). [ABSTRACT FROM AUTHOR]

In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion $H^1(\Omega)\hookrightarrow L^q(\partial\Omega)$ for functions that vanish in a subset of $\Omega$. This problem is also related to a minimization problem for Steklov eigenvalues. [ABSTRACT FROM AUTHOR]