Potpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization

Authors:
Jean-Baptiste Hiriart-Urruty
Affiliations:
-
Venue:
SIAM Review
Year:
2007

Citing 0
Cited 7

Bregman distances and Klee sets

Journal of Approximation Theory
Bregman distances and Chebyshev sets

Journal of Approximation Theory
The Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach spaces

Journal of Approximation Theory
Klee sets and Chebyshev centers for the right Bregman distance

Journal of Approximation Theory
Some Equivalent Results with Yakubovich's $S$-Lemma

SIAM Journal on Control and Optimization
The Legendre-Fenchel Conjugate of the Product of Two Positive Definite Quadratic Forms

SIAM Journal on Matrix Analysis and Applications
Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint

Journal of Global Optimization

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Abstract

We present a collection of fourteen conjectures and open problems in the fields of nonlinear analysis and optimization. These problems can be classified into three groups: problems of pure mathematical interest, problems motivated by scientific computing and applications, and problems whose solutions are known but for which we would like to know better proofs. For each problem we provide a succinct presentation, a list of appropriate references, and a view of the state of the art of the subject.