Results 121 to 130 of about 532 (159)
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Canadian Journal of Mathematics, 1950
Introduction. Let I be the closed real number interval: Any subset Δ of I containing at least one number interior to I, will be called a quasiconvexity generating set. To each quasiconvexity generating set Δ we associate as follows a generalized notion of convexity, here called quasiconvexity or Δ convexity.
Green, J. W., Gustin, W.
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Introduction. Let I be the closed real number interval: Any subset Δ of I containing at least one number interior to I, will be called a quasiconvexity generating set. To each quasiconvexity generating set Δ we associate as follows a generalized notion of convexity, here called quasiconvexity or Δ convexity.
Green, J. W., Gustin, W.
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Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives [PDF]
Optimization Letters, 2020 For a C-2-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict ...
Pham Duy Khanh +2 more
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Mathematical Programming, 2021
An essential goal of this paper is to find sufficient conditions or even characterizations for quasiconvex functions such that sum or minimum of two (or finitely many) such funtions are again quasiconvex. To do this, the authors use the connection between quasiconvex functions \(f\) and quasimonotone operators (think of \(\partial{f}\)), use a new ...
Fabián Flores Bazán +2 more
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An essential goal of this paper is to find sufficient conditions or even characterizations for quasiconvex functions such that sum or minimum of two (or finitely many) such funtions are again quasiconvex. To do this, the authors use the connection between quasiconvex functions \(f\) and quasimonotone operators (think of \(\partial{f}\)), use a new ...
Fabián Flores Bazán +2 more
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Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniilidis, A., Hadjisavvas, N.
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Semicontinuity and Quasiconvex Functions
Journal of Optimization Theory and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mukherjee, R. N., Reddy, L. V.
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Ray-quasiconvex and f-quasiconvex functions
1994Using the definition of ray in the euclidean space, we define a new class of functions that avoid Karamardian’s anomaly and which contain the quasimonotonic functions. These new functions have a good behaviour in relation to its optimal sets, allowing the construction of heuristic algorithms in order to find its extreme points.
J. A. Mayor-Gallego +2 more
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THE COMBINATION THEOREM AND QUASICONVEXITY
International Journal of Algebra and Computation, 2001We show that if G is a fundamental group of a finite k-acylindrical graph of groups where every vertex group is word-hyperbolic and where every edge-monomorphism is a quasi-isometric embedding, then all the vertex groups are quasiconvex in G (the group G is word-hyperbolic by the Combination Theorem of M. Bestvina and M. Feighn).
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Approximating Quasiconvex Functions with Strictly Quasiconvex Ones in Banach Space
Set-Valued and Variational Analysis, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucchetti, Roberto, Milasi, Monica
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Zeitschrift für Operations Research, 1983
In this article we develop a conjugacy theory in quasiconvex analysis, in which no lower semicontinuity or normality assumption is needed to ensure the coincidence of the second conjugate of any function with its quasivonvex hull. This is made by an extension of the concept ofH-conjugation, and is based on a separation theorem by general halfspaces ...
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In this article we develop a conjugacy theory in quasiconvex analysis, in which no lower semicontinuity or normality assumption is needed to ensure the coincidence of the second conjugate of any function with its quasivonvex hull. This is made by an extension of the concept ofH-conjugation, and is based on a separation theorem by general halfspaces ...
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Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
Advances in Calculus of Variations, 2015 Let K be a given compact set of real 2x2 matrices that is isotropic, meaning invariant under the leftand right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides withthe lamination convex hull of order 2.
Heinz, Sebastian
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