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Variational Subdifferential for Quasiconvex Functions
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The structure of quasiconvex functions
1998Abstract From Remark 5.17 we deduce that quasiconvexity is a sufficient condition for the lower semicontinuity of integral functionals with respect to the weak* convergence in W hence quasiconvex functions are rank-1-convex by Corollary 4.12.
Andrea Braides, Anneliese Defranceschi
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2020
This chapter is devoted to the study of those functions whose lower level sets are evenly convex, the so-called evenly quasiconvex functions. In Sect. 3.1 we define this class of functions, which provides greater minorants than the smaller class of the lower semicontinuous quasiconvex functions.
María D. Fajardo +3 more
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This chapter is devoted to the study of those functions whose lower level sets are evenly convex, the so-called evenly quasiconvex functions. In Sect. 3.1 we define this class of functions, which provides greater minorants than the smaller class of the lower semicontinuous quasiconvex functions.
María D. Fajardo +3 more
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On extremal points of quasiconvex functions
Mathematical Programming, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quadratic Programming with a Quasiconvex Objective Function
Operations Research, 1971This paper gives both necessary and sufficient conditions for a quadratic function to be quasiconvex in the nonnegative orthant. Methods of pseudoconvex programming (such as those of Frank and Wolfe) can solve linearly constrained quadratic programming problems with such an objective function.
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Functions With Quasiconvex Derivatives
1998The necessary and sufficient conditions for quasiconvexity are given for the derivative of real-valued function, defined and continuously differentiate on I = [a, b] ⊂ ℝ Also, some inequalities are presented in this paper.
Vidan Govedarica, Milan Jovanović
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On Generalized Pseudo- and Quasiconvexities for Nonsmooth Functions
2018Convexity is the most important and useful concept in mathematical optimization theory. In order to extend the existing results depending on convexity, numerous attempts of generalizing the concept have been published during years. Different types of generalized convexities have proved to be the main tool when constructing optimality conditions, in ...
Mäkelä Marko +2 more
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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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Level Function Method for Quasiconvex Programming
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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