Concave function

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

Method and apparatus for transductive support vector machines

Abstract: Disclosed is a method for training a transductive support vector machine The support vector machine is trained based on labeled training data and unlabeled test data A non-convex objective function which optimizes a hyperplane classifier for classifying the unlabeled test data is decomposed into a convex function and a concave function A local approximation of the concave function at a hyperplane is calculated, and the approximation of the concave function is combined with the convex function such that the result is a convex problem The convex problem is then solved to determine an updated hyperplane This method is performed iteratively until the solution converges

Numerical methods for optimal investment-consumption models

Abstract: Some stochastic control problems are considered which arise in an optimal investment-consumption context. These problems have the common feature that the optimal cost function, which satisfies a dynamic programming differential equation, is a concave function of the state. The purpose is to find good numerical approximations to the optimal cost function, as well as optimal investment and consumption policies, and to prove convergence of these approximations as the step size tends to zero. The special linear-concave structure of the problems results in stronger convergence than for more general classes of optimal stochastic control problems. The stronger convergence is obtained by partial differential equation viscosity solution methods rather than by the probabilistic-weak convergence techniques. It is expected that the methods developed with be applicable to wider classes of problems with linear-concave structure. >

Some extended Simpson-type inequalities and applications

Abstract: ‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time

Abstract: This paper suggests that introducing randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time. Concavity can make increased variability in waiting times good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum or if the customer incurs a fixed cost if there is any wait at all. As examples, cost might asymptotically approach a maximum for patients seeking organ transplants who will not live beyond a certain threshold time, and fixed costs could pertain for knowledge workers seeking a piece of information that is required to proceed with their current task, so any delay creates a “set up charge” associated with switching tasks.