Finite Dimensional Convexity and Optimization
@inproceedings{Florenzano2001FiniteDC, title={Finite Dimensional Convexity and Optimization}, author={Monique Florenzano and Cuong Le Van and Pascal Gourdel}, year={2001} }
Convexity in Rn.- Separation and Polarity.- Extremal Structure of Convex Sets.- Linear Programming.- Convex Functions.- Differential Theory of Convex Functions.- Convex Optimization With Convex Constraints.- Non Convex Optimization.- Appendix.
62 Citations
Convex Optimization
- Computer ScienceIEEE Transactions on Automatic Control
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A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.
A convex-valued selection theorem with a non-separable Banach space
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Abstract In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ : X → 2 Y {\varphi:X\to 2^{Y}} . We prove that if…
Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints
- Mathematics4OR
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In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and,…
A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions
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- 2018
In this paper basic results on sensitivity and stability analysis in differentiable nonlinear programming problems are surveyed. We follow mainly the approach of A. V. Fiacco and his co-authors. We…
SOME RESULT ON EXTREME POINTS IN ORDERED TOPOLOGICAL CONES
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- 2017
A cone theoretic Krein-Milman theorem states that in any locally convex T0 topological cone, every convex compact saturated subset is the compact saturated convex hull of its m-extreme points. In…
On Notations for Conic Hulls and Related Considerations on Tangent Cones
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We propose two different notations for cones generated by a set and for convex cones generated by a set, usually denoted by a same notation. We make some remarks on the Bouligand tangent cone and on…
Sections and projections of homothetic convex bodies
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- 2006
Abstract.For a pair of convex bodies K1 and K2 in Euclidean space
$$ \mathbb{E}^n $$, n ≥ 3, possibly unbounded, we show that K1 is a translate of K2 if either of the following conditions holds: (i)…
An antimaximum principle for periodic solutions of a forced oscillator
- MathematicsCommunications in Contemporary Mathematics
- 2022
. Consider the equation of the linear oscillator u ′′ + u = h ( θ ), where the forcing term h : R → R is 2 π -periodic and positive. We show that the existence of a periodic solution implies the…