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On Generating All Optimal Monotone Classifications
2011 IEEE 11th International Conference on Data Mining, 2011In many applications of data mining one knows beforehand that the response variable should be monotone (either increasing or decreasing) in the attributes. In ordinal classification, changing the class labels of a data set (relabeling) so that the data becomes monotone, is useful for at least two reasons.
Stegeman, L., Feelders, A.J.
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Monotonicity in Generalized Semi-Markov Processes
Mathematics of Operations Research, 1992We establish stochastic monotonicity of the event epoch sequences of generalized semi-Markov processes through the structure of the generalized semi-Markov schemes on which they are based. Our main condition states, roughly, that the occurrence of more events in the short run never leads to the activation of less events in the long run.
Paul Glasserman, David D. Yao
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Centers of Monotone Generalized Complementarity Problems
Mathematics of Operations Research, 1997Let C be a full dimensional, closed, pointed and convex cone in a finite dimensional real vector space ℰ with an inner product 〈x, y〉 of x, y ∈ ℰ, and ℳ a maximal monotone subset of ℰ × ℰ. This paper studies the existence and continuity of centers of the monotone generalized complementarity problem associated with C and ℳ: Find (x, y) ∈ ℳ ∩ (C × C ...
Masayuki Shida +2 more
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Generalized gradients of monotone type
Nonlinear Analysis: Theory, Methods & Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalizations of monotonicity
1994\textit{E. T. Copson} [Proc. Edinb. Math. Soc., II. Ser. 17, 159-164 (1970; Zbl 0223.40001)], showed that a bounded positive sequence \(\{a_ n\}\) satisfying \(a_{n+r}\leq \sum_{s=1}^ r k_ s a_{n+r-s}\), \(k_ s>0\), \(k_ 1+ \cdots+ k_ r =1\) \(\forall n\) is necessarily convergent. \textit{C. Rossi} [Monotonia alle Copson e sue generalizzazioni.
FIOCCHI, Cristina, ZANELLI, Vanna
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Generalized monotonicity and generalized convexity
Journal of Optimization Theory and Applications, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2006
We first present nine kinds of (generalized) monotone maps and in case of gradient maps their counterpart of nine kinds of (generalized) convex functions. In addition we present topologically pseudomonotone maps. We then derive sufficient and/or necessary conditions for various kinds of generalized monotonicity for several subclasses of maps.
Nicolas Hadjisavvas, Siegfried Schaible
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We first present nine kinds of (generalized) monotone maps and in case of gradient maps their counterpart of nine kinds of (generalized) convex functions. In addition we present topologically pseudomonotone maps. We then derive sufficient and/or necessary conditions for various kinds of generalized monotonicity for several subclasses of maps.
Nicolas Hadjisavvas, Siegfried Schaible
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Variational Inequalities with Generalized Monotone Operators
Mathematics of Operations Research, 1994We investigate the variational inequality with pseudomonotone operators (in the sense of Karamardian) in Banach spaces. New existence results which extend many known results in infinite-dimensional spaces are derived under rather weak assumptions. New uniqueness results which also seem to be new even in finite-dimensional spaces are also derived.
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Pseudo-Monotonicity and Generalized Pseudo-Monotonicity
2021Z. Naniewicz, P. D. Panagiotopoulos
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Nine Kinds of Monotone and Generalized Monotone Maps
1994Monotonicity plays an important role in complementarity problems and variational inequality problems, like convexity in mathematical programming. Recently, seven kinds of monotone and generalized monotone maps were introduced; see Karamardian et al. (1990).
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