# 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
- 2006

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

- 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

- Mathematics4OR
- 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

- Mathematics
- 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)…

### 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…