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While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
While making informed decisions regarding
investments in customer retention and acquisition becomes a
pressing managerial issue, formal models and analysis, which may
provide insight into this topic, are still scarce. In this study
we examine two dynamic models for optimal acquisition and
retention models of a monopoly, the total cost and the cost per
customer models.
These models are analytically analyzed using classical, direct,
methods and asymptotic expansions (for the total cost model).
In...
We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.
In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under...
We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we...
Updating probabilities by information from only one hypothesis and thereby ignoring alternative hypotheses, is not only biased but leads to progressively imprecise conclusions. In psychology this phenomenon was studied in experiments with the “pseudodiagnosticity task”. In probability logic the phenomenon that additional premises increase the imprecision of a conclusion is known as “degradation”. The present contribution investigates degradation in the context of second order probability distributions....
This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control...
This review aims at presenting a
synoptic, if not exhaustive, point of view on some of the problems
encountered by biologists and physicians who deal with natural
cell proliferation and disruptions of its physiological control in
cancer disease. It also aims at suggesting how mathematicians are
naturally challenged by these questions and how they might help,
not only biologists to deal theoretically with biological
complexity, but also physicians to optimise therapeutics, on which
last point the...
In a recent paper [Forum Math., 2008] the authors established some global, up to the boundary of a domain Ω ⊂ ℝⁿ, continuity and Morrey regularity results for almost minimizers of functionals of the form . The main assumptions for these results are that g is asymptotically convex and that it satisfies some growth conditions. In this article, we present a specialized but significant version of this general result. The primary purpose of this paper is provide several applications of this simplified...
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