Showing papers on "Isotone published in 2012"
TL;DR: This paper presents an explicit characterization of the convex hull of the feasible region when the MINLP consists of simple bounds on the variables and one “on/off” constraint defined by an isotone function f.
Abstract: In this paper, we study MINLPs featuring "on/off" constraints. An "on/off" constraint is a constraint f(x)?0 that is activated whenever a corresponding 0---1 variable is equal to 1. Our main result is an explicit characterization of the convex hull of the feasible region when the MINLP consists of simple bounds on the variables and one "on/off" constraint defined by an isotone function f. When extended to general convex MINLPs, we show that this result yields tight lower bounds compared to classical formulations. This allows us to introduce new models for the delay-constrained routing problem in telecommunications. Numerical results show gains in computing time of up to one order of magnitude compared to state-of-the-art approaches.
67 citations
TL;DR: The result is presented that it is not the availability of the law of double negation but rather the fact that negations are implicitly present in the construction of concept lattices of isotone Galois connections that reveals a new, deeper root of the reduction.
33 citations
TL;DR: In this article, Iterative methods for finding solutions of complementarity problems on *-isotone projection cones are presented and the problem of finding nonzero solutions of these problems is also considered.
24 citations
TL;DR: In this paper, an iterative algorithm is presented in connection with an implicit complementarity problem on *-isotone projection cones and it is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementary problem.
Abstract: Isac and Nemeth [G. Isac and A. B. Nemeth, Projection method, isotone projection cones and the complementarity problem, J. Math. Anal. App., 153, 258-275(1990)] proved that solving a coincidence point equation (fixed point problem) in turn solves the corresponding implicit complementarity problem (nonlinear complementarity problem) and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems (nonlinear complementarity problems) defined by these cones. In this paper, the notion of *-isotone projection cones is employed and an iterative algorithm is presented in connection with an implicit complementarity problem on *-isotone projection cones. It is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem. Sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by *-isotone projection cones. The question of finding nonzero solutions of these problems is also studied.
22 citations
TL;DR: In this paper, the authors investigated the properties of derivations in lattices and established characterizations of a chain, a distributive lattice, a modular lattice and a relatively pseudo-complemented lattice.
Abstract: The related properties of derivations in lattices are investigated. We show that the set of all isotone derivations in a distributive lattice can form a distributive lattice. Moreover, we introduce the fixed set of derivations in lattices and prove that the fixed set of a derivation is an ideal in lattices. Using the fixed sets of isotone derivations, we establish characterizations of a chain, a distributive lattice, a modular lattice and a relatively pseudo-complemented lattice, respectively. Furthermore, we discuss the relations among derivations, ideals and fixed sets in lattices.
20 citations
TL;DR: In this article, the authors set up two new variants of ψ-contractive mappings designed for two and three maps in metric spaces and originate common fixed point theorems for -strictly weakly isotone increasing mappings and relatively weakly increasing mapping in complete ordered metric spaces.
Abstract: We set up two new variants of ψ-contractive mappings designed for two and three maps in metric spaces and originate common fixed point theorems for -strictly weakly isotone increasing mappings and relatively weakly increasing mappings in complete ordered metric spaces. To demonstrate our results, we give some examples throughout the paper. At the same time, as applications of the presented theorems, we get hold of common fixed point results for generalized contractions of integral type and we prove an existence theorem for solutions of a system of integral equations. MSC:47H10, 45F05.
6 citations
TL;DR: In this article, the notion of isotone projection cones was extended to generalized isotone projections by replacing the usual metric projection with a generalized one and it was shown that all such cones are simplicial.
Abstract: This article extends the notion of isotone projection cones to generalized isotone projection cones by replacing the usual metric projection with a generalized one It is shown that all such cones are simplicial
6 citations
TL;DR: In this article, an iterative algorithm is studied in connection with an implicit complementarity problem, and it is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementary problem.
Abstract: Isac and Nemeth [G. Isac and A. B. Nemeth, Projection methods, isotone projection cones and the complementarity problem, J. Math. Anal. Appl. 153 (1990), pp. 258–275] proved that solving a coincidence point equation (fixed point problem) in turn solves the corresponding implicit complementarity problem (nonlinear complementarity problem) and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems (nonlinear complementarity problems) defined by these cones. In this article an iterative algorithm is studied in connection with an implicit complementarity problem. It is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem. Sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by isotone projection cones, extending the results of Nemeth ...
6 citations
TL;DR: In this article, the authors extend the notion of weakly isotone increasing mappings to multivalued and present common endpoint theorems for -weakly-isotone increasing multiivalued mappings satisfying generalized -weak contractive as well as almost contractive inequalities in complete partially ordered metric spaces.
Abstract: The aim of this work is to extend the notion of weakly isotone increasing mappings to multivalued and present common endpoint theorems for -weakly isotone increasing multivalued mappings satisfying generalized -weak contractive as well as almost contractive inequalities in complete partially ordered metric spaces. Examples are given in support of the new results obtained. MSC:47H10, 54H25, 54H10.
5 citations
01 Jan 2012
TL;DR: The present article shall elaborate the inner type development of MI sections 14 and 15 into parallel outer and inner representation theories, as formulated in MI0 section 3 as the decisive point for the purpose of that paper.
Abstract: The present article is another continuation of the recent book of the author [1997] on measure and integration (cited as MI). The subsequent expository paper [1999] (cited as MI0) summarized the essentials, and went on to attain a standpoint which permits the competent evaluation of the traditional extension theories named after Daniell-Stone and Bourbaki, that is of those which start with certain isotone linear functionals. To this end the paper described without proof some further developments. The present article and its predecessor [1998] (cited as MI1) have the aim to elaborate these new developments in adequate contexts. While the previous one dealt with the measure-theoretic aspects proper as described in MI0 sections 1 and 4, the topic this time are certain isotone functionals and their integral representations. We shall elaborate the inner type development of MI sections 14 and 15 into parallel outer and inner representation theories, as formulated in MI0 section 3 as the decisive point for the purpose of that paper.
4 citations
TL;DR: The purpose of this paper is to prove end-point theorems for multivalued mappings satisfying comparatively a more general contractive condition in ordered complete metric spaces.
Abstract: The purpose of this paper is to prove end-point theorems for multivalued mappings satisfying comparatively a more general contractive condition in ordered complete metric spaces. Afterwards, we extend the results of previous sections and prove common end-point results for a pair of 𝒯-weakly isotone increasing multivalued mappings in the underlying spaces. Finally, we present common end point for a pair of 𝒯-weakly isotone increasing multivalued mappings satisfying weakly contractive condition.
01 Oct 2012
TL;DR: In this article, the authors generalize earlier work by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context.
Abstract: Suggested by conversations in 1991 (Mark Krasnosel'skiĭ and Aleksei Pokrovskiĭ with TIS), this paper generalizes earlier work [7] of theirs
by defining a setting of hybrid systems with isotone switching rules
for a partially ordered set of modes and then obtaining a periodicity
result in that context. An application is given to a partial
differential equation modeling calcium release and diffusion in
cardiac cells.
TL;DR: It will be shown that if the ordered set is a finite co-tree, then the universal predictor for the model or, equivalently, the corresponding universal code, can be determined exactly via an algorithm of low complexity.
Abstract: For an ordered set, consider the model of distributions P for which an element that precedes another element is considered the more significant one in the sense that the implication a ≤ b⇒ P(a) ≥ P(b) holds. It will be shown that if the ordered set is a finite co-tree, then the universal predictor for the model or, equivalently, the corresponding universal code, can be determined exactly via an algorithm of low complexity. Natural relations to problems on the computation of capacity and on the determination of information projections are established. More surprisingly, a direct connection to a problem of isotone regression also appears possible.
TL;DR: In this paper, the authors generalize earlier work by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context.
Abstract: Suggested by conversations in 1991 (Mark Krasnosel'skiĭ and Aleksei Pokrovskiĭ with TIS), this paper generalizes earlier work [7] of theirs
by defining a setting of hybrid systems with isotone switching rules
for a partially ordered set of modes and then obtaining a periodicity
result in that context. An application is given to a partial
differential equation modeling calcium release and diffusion in
cardiac cells.
01 Jan 2012
TL;DR: In this article, the authors generalize earlier work by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context.
Abstract: Suggested by conversations in 1991 (Mark Krasnosel’skiı̆ and Aleksei Pokrovskiı̆ with TIS), this paper generalizes earlier work [7] of theirs by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context. An application is given to a partial differential equation modeling calcium release and diffusion in cardiac cells.
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TL;DR: In this paper, it was shown that the monotone wedge admits isotone projection with respect to the semi-order induced by them, and the obtained result was used to show that the Monotone cone admits the same.
Abstract: A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges admitting isotone metric projection with respect to the semi-order induced by them are characterized. The obtained result is used to show that the monotone wedge (called monotone cone in regression theory) admits isotone projection.