Topic
Concave function
About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.
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TL;DR: In this article, the authors show that for a special function, which is proportional to the density of a Wishart distribution, reparametrization can lead to maximization of a concave function.
5 citations
TL;DR: The relationships between the error bound and the exact penalization are investigated and the new error bounds for inequality systems of concave functions and of nonconvex quadratic functions over polyhedral convex sets are established.
Abstract: In this paper, we deal with the error bounds for inequality systems and the exact penalization for constrained optimization problems. We firstly investigate the relationships between the error bound and the exact penalization. Then we establish the new error bounds for inequality systems of concave functions and of nonconvex quadratic functions over polyhedral convex sets.
5 citations
TL;DR: In the domain of multidimensional single-peaked preferences, it is found that any allocation mechanism obtained by maximizing a separably concave function over a polyhedral extension of the set of Pareto-efficient allocations is strategy-proof.
5 citations
Posted Content•
TL;DR: The key idea of the algorithm is to learn the input data pattern dynamically: it solves a sequence of carefully chosen partial allocation problems and use their optimal solutions to assist with the future decision.
Abstract: We consider an online matching problem with concave returns. This problem is a significant generalization of the Adwords allocation problem and has vast applications in online advertising. In this problem, a sequence of items arrive sequentially and each has to be allocated to one of the bidders, who bid a certain value for each item. At each time, the decision maker has to allocate the current item to one of the bidders without knowing the future bids and the objective is to maximize the sum of some concave functions of each bidder's aggregate value. In this work, we propose an algorithm that achieves near-optimal performance for this problem when the bids arrive in a random order and the input data satisfies certain conditions. The key idea of our algorithm is to learn the input data pattern dynamically: we solve a sequence of carefully chosen partial allocation problems and use their optimal solutions to assist with the future decision. Our analysis belongs to the primal-dual paradigm, however, the absence of linearity of the objective function and the dynamic feature of the algorithm makes our analysis quite unique.
5 citations
Journal Article•
TL;DR: In this paper, a new class of extended (m 1,m 2)-convex and concave functions is introduced, and the inequalities obtained with Holder and Holder-Iscan and power-mean and improwed power mean integral inequalities have been compared.
Abstract: In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Holder and Holder-Iscan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Holder-Iscan inequality gives a better approach than with Holder integral inequality and improwed power-mean inequality gives a better approach than with power-mean inequality.
5 citations