# 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.

## 56 Citations

Convex Optimization

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2006

A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.

The Dual Approach to Recursive Optimization: Theory and Examples

- Computer Science
- 2014

This work provides a dual version of the principle of optimality and gives conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point.

The Dual Approach to Recursive Optimization: Theory and Examples

- Mathematics
- 2018

We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the…

A convex-valued selection theorem with a non-separable Banach space

- Mathematics
- 2016

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

- Mathematics
- 2021

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

- Mathematics
- 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

- 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

- Mathematics
- 2021

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

- Mathematics
- 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)…

The existence of equilibrium without fixed-point arguments

- Economics
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Abstract This paper gives a proof of the existence of general equilibrium without the use of a fixed point theorem. Unlike other results of this type, the conditions we use do not imply that the set…