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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, a method of consistently estimating a representative of a concave and monotone nonparametric systematic function is presented, where the representative possesses the same isovalue sets as the systematic function.
Abstract: This paper studies the estimation of fully nonparametric models in which we can not identify the values of a symmetric function that we seek to estimate. I develop a method of consistently estimating a representative of a concave and monotone nonparametric systematic function. This representative possesses the same isovalue sets as the systematic function. The method proceeds by characterizing each set of observationally equivalent concave functions by a unique "least concave" representative. The least concave representative of the equivalence class to which the systematic function belongs is estimated by maximizing a criterion function over a compact set of least concave functions. I develop a computational technique to evaluate the values, at the observed points, and the gradients, at every point and up to a constant, of this least concave estimator. The paper includes a detailed description of how the method can be used to estimate three popular microeconometric models.
9 citations
TL;DR: The concept of a γ-valid cutting plane has been used in many types of algorithms for solving concave minimization problems as mentioned in this paper, but these procedures are valid only under certain assumptions that often may not hold in practice.
Abstract: The concept of a γ-valid cutting plane has been used in many types of algorithms for solving concave minimization problems. Unfortunately, the procedures proposed to date for constructing these cuts are valid only under certain assumptions that often may not hold in practice. Chief among these is the requirement that the feasible region of the concave minimization problem in question have full dimension, and that the objective function of this problem be concave rather than quasiconcave. In this article, we propose, validate, and show how to implement a more general γ-valid cutting plane procedure which eliminates these restrictions.
9 citations
23 Oct 2016
TL;DR: The classical Jensen inequality for concave function \(\varphi \) is adapted for the Sugeno integral using the notion of the subdifferential using the framework of the Lebesgue measure.
Abstract: The classical Jensen inequality for concave function \(\varphi \) is adapted for the Sugeno integral using the notion of the subdifferential. Some examples in the framework of the Lebesgue measure to illustrate the results are presented.
9 citations
TL;DR: An algorithm is given that finds an epsilon-approximate solution for the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron by solving a number of integer linear programs whose constraint matrices have subdeterminants bounded by D in absolute value.
Abstract: We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by $\Delta$ the largest absolute value of the subdetermi...
9 citations
TL;DR: An example of a convex function having the gradient at each point (x, 0,..., 0),x>0, which does not converge, whenx tends to zero, is given in this article.
Abstract: An example of a convex function having the gradient at each point (x, 0, ..., 0),x>0, which does not converge, whenx tends to zero, is given.
9 citations