Results 151 to 160 of about 430 (171)
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Minimization of Quasiconvex Functions
2020In this chapter we study minimization of a quasiconvex function. Our algorithm has two steps. In each of these two steps there is a computational error. In general, these two computational errors are different. We show that our algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive ...
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New examples of quasiconvex functions
Archive for Rational Mechanics and Analysis, 1992Let \({\mathcal S}_ n\) denote the space of all symmetric \(n\times n\) matrices and let \({\mathcal O}_ l\) be the subset of the regular matrices with index \(l\), \(0\leq l\leq n\). The author proves that the functions \(F_ l: {\mathcal S}_ n\to {\mathcal R}\) defined by \[ F_ l(X)= \begin{cases} |\text{det } X|\quad & \text{if }X\in {\mathcal O}_ l\\
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Quasidifferentiability of nonsmooth quasiconvex functions
Optimization, 1993The paper deals with nonsmooth quasiconvex functions and develops a quasidifferential analysis for this class of functions. Therefore, in terms of sub and superdifferentials, first order approximations of the functions are derived, optimality conditions are stated and directions of descent (either simple feasible or of steepest descent) are determined.
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Quasiconvex functions with subquadratic growth
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991Abstract We establish the existence of quasiconvex functions which are not convex and which have subquadratic grow that infinity.
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Directional derivatives of quasiconvex functionals
Journal of Soviet Mathematics, 1988We show that a directional derivative of a quasiconvex functional is also a quasiconvex functional. In this connection we study properties of quasiconvex and positively homogeneous functionals.
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On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms
Journal of Optimization Theory and Applications, 2022Felipe Lara, Lara F
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Continuity and Differentiability of Quasiconvex Functions
2006The convexity of the epigraph of a convex function induces important properties with respect to the continuity and differentiability of the function. Moreover, the function is locally Lipschitz in the interior of the domain of the function. If for a quasiconvex function, the convexity concerns the lower level sets and not the epigraph, some important ...
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On a Theorem of Deák Concerning the Quasiconvexity of Semicontinuous-Quasiconvex Functions
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1980openaire +1 more source
Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set
Mathematical Notes, 2022S I Dudov, Dudov S I
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Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions
Vietnam Journal of Mathematics, 2020M Volle +2 more
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