Topic
Solution set
About: Solution set is a research topic. Over the lifetime, 3742 publications have been published within this topic receiving 62157 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.
1,749 citations
••
31 Dec 1978
TL;DR: On stable properties of the solution set of an ordinary differential equation, see as mentioned in this paper and the Morse index continuuation bibliography for a complete survey of the literature on flow stability and flow properties.
Abstract: On stable properties of the solution set of an ordinary differential equation Elementary properties of flows The Morse index Continuation Bibliography.
1,662 citations
••
TL;DR: In this article, the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem, and develop practical methods for checking the condition.
Abstract: The authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist, consumer and growth theory, game theory, and general equilibrium analysis. Copyright 1994 by The Econometric Society.
1,526 citations
••
19 Aug 2002TL;DR: A new definition of distance-based outlier that considers for each point the sum of the distances from its k nearest neighbors, called weight, is proposed, which scales linearly both in the dimensionality and the size of the data set.
Abstract: In this paper we propose a new definition of distance-based outlier that considers for each point the sum of the distances from its k nearest neighbors, called weight. Outliers are those points having the largest values of weight. In order to compute these weights, we find the k nearest neighbors of each point in a fast and efficient way by linearizing the search space through the Hilbert space filling curve. The algorithm consists of two phases, the first provides an approximated solution, within a small factor, after executing at most d + 1 scans of the data set with a low time complexity cost, where d is the number of dimensions of the data set. During each scan the number of points candidate to belong to the solution set is sensibly reduced. The second phase returns the exact solution by doing a single scan which examines further a little fraction of the data set. Experimental results show that the algorithm always finds the exact solution during the first phase after d ? d + 1 steps and it scales linearly both in the dimensionality and the size of the data set.
751 citations
•
30 Sep 1995
TL;DR: This paper presents a meta-anatomy of null-additive set functions based on decomposable measures and some examples show how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Abstract: Preface. 1. Introduction. 2. Null-additive set functions. 3. Autocontinuity of null-additive set functions. 4. Atoms of null-additive set functions. 5. Choquet and Sugeno integral. 6. Lebesgue decomposition and regularity of null-additive set functions. 7. The range of null-additive set function. 8. k-Triangular set functions. 9. Uniform space valued set functions. 10. Integrals based on decomposable measures. References. Index.
728 citations