Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.

Coefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functions

Abstract: In this article, we discuss the coefficient regions of analytic self-maps of the unit disk with a prescribed fixed point. As an application, we solve the Fekete–Szegő problem for normalized concave functions with a pole in the unit disk.

Conical algorithm for the global minimization of linearly constrained decomposable concave minimization problems

Abstract: In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on ap-dimensional space and a linear function defined on aq-dimensional space, whereq may be much larger thanp. It is shown that a conical algorithm can be applied in a space of dimensionp + 1 that involves only linear programming subproblems in a space of dimensionp +q + 1. Some computational results are given.

Integrated inventory and transportation decision for ubiquitous supply chain management

Abstract: We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.

Ascending auctions for integral (poly)matroids with concave nondecreasing separable values

Abstract: Consider a seller with a fixed set of resources that can produce a variety of bundles from a set E of indivisible goods. Several bidders are interested in purchasing a bundle of such goods. Their utility for a bundle is privately known and represented by an additively separable, nondecreasing and concave function. In the case when the set of feasible bundles forms an integral polymatroid (or its basis), we present an ascending auction which in equilibrium returns the efficient outcome. Formally, given an integral, monotone, submodular function ρ: E → N0 with ρ(θ) = 0 the integral points of the polymatroid Pρ represent various allocations which the seller can feasibly offer. Buyers j ∈ N have privately known valuations vj (xj) for xj ∈ Pρ with the property that vj (xj) = Σe∈Evje(xje) where the vje(xje) are nondecreasing and concave. We present an ascending auction running in pseudo-polynomial time in which truthful bidding is an ex post equilibrium and results in the efficient outcome. Our auction strictly generalizes the ascending auction of Demange, Gale, and Sotomayor (1986) applied to scheduling matroids (agents want to schedule several jobs; their due and release dates are common knowledge, but the value of completing a job is private information). For a suitable class of uniform matroids, our auction reduces to the ascending auction of Ausubel (2004) for the allocation of multiple units of a homogeneous good when agents have decreasing marginal values in quantities. Finally, our auction can be applied to the setting of spatially distributed markets considered in Babaioff, Nisan, and Pavlov (2004).

Generalized Concavity for Bicriteria Functions

Abstract: In this paper some classes of vector valued generalized concave functions will be compared in the bicriteria case, that is when the images of the functions are contained in ℜ2. We will prove that, in the bicriteria case, continuous (C,C)-quasiconcave functions coincide with C-quasiconcave functions introduced by Luc; we will also prove that (C,C)-quasiconcave functions have a first order characterization and that they can be characterized by means of their increasness and decreasness.