Related papers: A new geometric approach for sensitivity analysis …
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
R\'esum\'e Apr\`es un bref aper\c{c}u permettant de situer notre travail, nous proposons une nouvelle voie pour aborder la programmation lin\'eaire en proposant un algorithme \'elabor\'e \`a partir d'une id\'ee simple qui permet d'obtenir…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
We discuss the issue of finding a good mathematical programming solver configuration for a particular instance of a given problem, and we propose a two-phase approach to solve it. In the first phase we learn the relationships between the…
We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input…
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…
We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
Observational studies provide invaluable opportunities to draw causal inference, but they may suffer from biases due to pretreatment difference between treated and control units. Matching is a popular approach to reduce observed covariate…
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…
Reducing the dimensionality and uncertainty of design spaces is a key prerequisite for shape optimisation in computationally intensive fluid problems. However, running these analyses at an offline stage itself poses a computationally…