Results 51 to 60 of about 88 (74)
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Maximal quasimonotonicity and dense single-directional properties of quasimonotone operators
Mathematical Programming, 2013Let \(X\) be a Banach space with topological dual \(X^*\). A set-valued operator \(T: X\rightrightarrows X^*\) with effective domain \(\text{Edom\,}T= \{x\in\text{dom\,}T: T(x)\neq\{0\}\) is called quasimonotone if, for all \(x,y\in\text{Edom\,} T\), \[ \exists x^*\in T(x): \langle x^*, y-x\rangle> 0\Rightarrow\forall y^*\in T(y):\langle y^*,y- x ...
Didier Aussel +2 more
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Continuity and maximal quasimonotonicity of normal cone operators
Studia Universitatis Babes-Bolyai Matematica, 2022In this paper we study some properties of the adjusted normal cone operator of quasiconvex functions. In particular, we introduce a new notion of maximal quasimotonicity for set-valued maps different from similar ones recently appeared in the literature, and we show that it is enjoyed by this operator.
Bianchi Monica +2 more
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Quasimonotonicity of Separable Operators and Monotonicity Indices
SIAM Journal on Optimization, 1994Summary: This research concerns the conditions that ensure the quasimonotonicity of the separable operator \(F(x_ 1,x_ 2,\dots, x_ p)= (F_ 1(x_ 1), F_ 2(x_ 2),\dots, F_ p(x_ p))\), where for \(i= 1,2,\dots, p\), \(C_ i\) is an open convex subset of \(\mathbb{R}^{n_ i}\) and \(F_ i: C_ i\to \mathbb{R}^{n_ i}\) is a continuous nonnull operator.
Jean-Pierre Crouzeix, Abdelhak Hassouni
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One-sided estimates for linear quasimonotone increasing operators
Numerical Functional Analysis and Optimization, 1998Let a Banach space E be ordered by a normal solid cone. In case A is a continuous quasimonotone increasing operator we prove that , for a single strictly positive element p, implies for a suitable chosen norm and all x in E. We give some application to ordinary and partial differential equations.
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On Single-Valuedness of Quasimonotone Set-Valued Operators
2017A Nash problem is a noncooperative game in which the objective function of each player also depends on the decision variable of the other player. In order to solve such difficult problem, a classical approach is to write the optimality conditions of each of the problems obtaining thus a variational inequality.
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Closedness under addition for families of quasimonotone operators
Optimization, 2022Fabián Flores-Bazán +2 more
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On the quasimonotonicity of a square linear operator with respect to a nonnegative cone
2012Major, United States ...
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A simple projection method for solving quasimonotone variational inequality problems
Optimization and Engineering, 2022Chinedu Izuchukwu +2 more
exaly
Strong convergence results for quasimonotone variational inequalities
Mathematical Methods of Operations Research, 2022Timilehin Opeyemi Alakoya +2 more
exaly