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Quasi-convex functions on subspaces and boundaries of quasi-convex sets
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004We embed truncations of the epi-graph of quasi-convex functions defined on linear subspaces E ⊂ MN × n of real matrices into MN × n to bound quasi-convex sets by the graph of the functions. We also characterize subspaces E on which all quasi-convex functions are convex and show, by using the Tarski–Seidenberg theorem in real algebraic geometry, that if
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Quasi-convex Functions in Carnot Groups*
Chinese Annals of Mathematics, Series B, 2007The authors introduce the concept of \(h\)-quasiconvexity which generalizes the notion of \(h\)-convexity in the Carnot group \(G\). An example of \(h\)-quasiconvex function which is not \(h\)-convex is provided. Some interesting properties similar to those of \(h\)-convex functions on \(G\) are given.
Sun, Mingbao, Yang, Xiaoping
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Structure of locally convex quasi C * -algebras
Journal of the Mathematical Society of Japan, 2008 The completion of a (normed) C*-algebra A0[∥ · ∥0] with respect to a locally convex topology τ on A 0 that makes the multiplication of A0 separately continuous is, in general, a quasi *-algebra, and not a locally convex *-algebra [10], [15]. In this way,
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Quasi Convex-Concave Extensions
2001Convexity and its generalizations have been considered in many publications during the last decades. In this paper we discuss the problem of bounding functions from below by quasiconvex functions and from above by quasiconcave functions. Moreover, applications fur nonlinear systems and constrained global optimization problems are considered briefly.
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Notes on Quasi-Convexity of the Cost Function
The Scandinavian Journal of Economics, 1984\textit{R. Shephard} [''Indirect production functions'' (1974; Zbl 0278.90036)] and \textit{S. E. Jacobsen} [J. Econ. Stud. 1972, 458-464 (1972)] have shown that the cost function is convex if and only if the production technology of a firm is convex.
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Surrogate Programming and Multipliers in Quasi-convex Programming
SIAM Journal on Control and Optimization, 2004Summary: A result due to \textit{D. G. Luenberger} [SIAM J. Appl. Math. 16, 1090--1095 (1968; Zbl 0212.23905)] on the existence of multipliers in a quasi-convex programming problem is extended to the case of constraints given by an arbitrary convex cone under a constraint qualification condition more general than Slater's condition.
Jean-Paul Penot, Michel Volle
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Minima of quasi-convex functions
Optimization, 1989This paper presents, in finite dimensions, some basic stability results for minima of proper, lower semicontinuous, quasi-convex functions with respect to the topology of epic on verge nee. Equipped with this topology the proper, lower semicontinuous, quasi-convex functions form a Baire space, and most such functions have unique minimizers (in the ...
G. Beer, R. Lucchetti
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2009
In this chapter, we define a new class of subsets of a Hilbert space, called the quasi-convex sets to which properties (i) (uniqueness), (iii) (stability) and (iv) (existence as soon as the set is closed) of Proposition 4.1.1 can be generalized, provided they are required to hold only on some neighborhood. Technically, the whole chapter will consist in
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In this chapter, we define a new class of subsets of a Hilbert space, called the quasi-convex sets to which properties (i) (uniqueness), (iii) (stability) and (iv) (existence as soon as the set is closed) of Proposition 4.1.1 can be generalized, provided they are required to hold only on some neighborhood. Technically, the whole chapter will consist in
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Locally Uniformly Quasi-Convex Programming
SIAM Journal on Applied Mathematics, 1975If X is a convex subset of a locally convex Hausdorif topological vector space $( {E,\tau } )$ and f is a real-valued $\tau $-l.s.c. quasi-convex functional on X, then f is also weakly l.s.c. on X and thus attains its infimum on X whenever X is weakly compact.
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Quasi-convex programming revisited
Calcolo, 1984This article deals with necessary and sufficient conditions of optimality for a nonlinear programming problem with quasi-convex objective and constraint functions. It is strictly related to a paper by \textit{S. Mititelu} [Rev. Roum. Math. Pures Appl. 21, 903-909 (1976; Zbl 0351.90058)] and provides new proofs of two theorems given in Mititelu's paper ...
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