1087. A derivative-free algorithm based on resilient positive spanning sets
Invited abstract in session TC-35: Recent trends in zeroth order and simulation-based optimization: 1, stream Continuous and mixed-integer nonlinear programming: theory and algorithms.
Tuesday, 12:30-14:00Room: Michael Sadler LG15
Authors (first author is the speaker)
| 1. | Sébastien Kerleau
|
| LAMSADE, Université Paris Dauphine PSL |
Abstract
Positive spanning sets (PSSs) are sets of vectors spanning the Euclidian space using non-negative linear combinations. They can also be defined as sets properly approximating any given direction in the space and as such they prove very useful in derivative-free optimization algorithms. Optimization methods based on PSSs typically favor those with the best cosine measure, as this implies that the elements of the PSS are well spread. However, this metric does not fully account for the structure of the PSS: in particular, it does not reflect the spanning capabilities of a given subset of the PSS vectors. In this talk, I will focus on a particular subclass of PSSs, called positive k-spanning sets. A positive k-spanning set (PkSS) remains positively spanning when some of its elements are removed. After formally defining the positive k-spanning property, I will provide a simple method to construct PkSSs whose subsets possess a large cosine measure. Using such sets, I will introduce a derivative-free algorithm based on parallel computing, that will prove to be resilient to stragglers or even failures of parallel evaluations.
Keywords
- Continuous Optimization
Status: accepted
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