ORCID Profile
0000-0002-5456-0180
Current Organisation
Monash University
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In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Optimisation | Numerical and Computational Mathematics |
Expanding Knowledge in Engineering | Expanding Knowledge in the Mathematical Sciences
Publisher: IEEE
Date: 06-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2015
DOI: 10.1137/140966265
Publisher: IEEE
Date: 12-2017
Publisher: IEEE
Date: 07-2016
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2020
DOI: 10.1137/19M1245670
Publisher: Elsevier BV
Date: 2017
Publisher: Springer Science and Business Media LLC
Date: 06-03-2017
Publisher: American Institute of Aeronautics and Astronautics (AIAA)
Date: 2015
DOI: 10.2514/1.G001107
Publisher: IEEE
Date: 12-2013
Publisher: Springer Science and Business Media LLC
Date: 21-03-2018
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2019
DOI: 10.1137/19M1253551
Publisher: IEEE
Date: 03-2016
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2019
DOI: 10.1137/18M1217152
Publisher: Springer Science and Business Media LLC
Date: 13-08-2015
Publisher: Springer Science and Business Media LLC
Date: 05-03-2018
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 02-2023
Abstract: Every convex homogeneous polynomial (or form) is nonnegative. Blekherman has shown that there exist convex forms that are not sums of squares via a nonconstructive argument. We provide an explicit ex le of a convex form of degree 4 in 272 variables that is not a sum of squares. The form is related to the Cauchy-Schwarz inequality over the octonions. The proof uses symmetry reduction together with the fact (due to Blekherman) that forms of even degree that are near-constant on the unit sphere are convex. Using this same connection, we obtain improved bounds on the approximation quality achieved by the basic sum-of-squares relaxation for optimizing quaternary quartic forms on the sphere. Funding: This work was supported by the Australian Research Council [Grant DE210101056].
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/14096339X
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2021
DOI: 10.1137/20M1358037
Publisher: Springer Science and Business Media LLC
Date: 27-01-2016
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 11-2022
DOI: 10.1137/20M1324417
Publisher: IEEE
Date: 12-2011
Publisher: Royal Society of Chemistry (RSC)
Date: 2023
DOI: 10.1039/D2PY01531E
Abstract: Using ridge regression, the propagation rate coefficients for radical polymerization are correlated with basic molecular properties.
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 03-2023
Publisher: Springer Science and Business Media LLC
Date: 12-06-2018
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 05-2017
Abstract: Given a polytope P ⊂ ℝ n , we say that P has a positive semidefinite lift (psd lift) of size d if one can express P as the projection of an affine slice of the d × d positive semidefinite cone. Such a representation allows us to solve linear optimization problems over P using a semidefinite program of size d and can be useful in practice when d is much smaller than the number of facets of P. If a polytope P has symmetry, we can consider equivariant psd lifts, i.e., those psd lifts that respect the symmetries of P. One of the simplest families of polytopes with interesting symmetries is regular polygons in the plane. In this paper, we give tight lower and upper bounds on the size of equivariant psd lifts for regular polygons. We give an explicit construction of an equivariant psd lift of the regular 2 n -gon of size 2n − 1, and we prove that our construction is essentially optimal by proving a lower bound on the size of any equivariant psd lift of the regular N-gon that is logarithmic in N. Our construction is exponentially smaller than the (equivariant) psd lift obtained from the Lasserre/sum-of-squares hierarchy, and it also gives the first ex le of a polytope with an exponential gap between equivariant psd lifts and equivariant linear programming lifts.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 09-2022
DOI: 10.1137/20M138466X
Publisher: Springer Science and Business Media LLC
Date: 05-03-2023
DOI: 10.1007/S10107-022-01774-Y
Abstract: We present a generalization of the notion of neighborliness to non-polyhedral convex cones. Although a definition of neighborliness is available in the non-polyhedral case in the literature, it is fairly restrictive as it requires all the low-dimensional faces to be polyhedral. Our approach is more flexible and includes, for ex le, the cone of positive-semidefinite matrices as a special case (this cone is not neighborly in general). We term our generalization Terracini convexity due to its conceptual similarity with the conclusion of Terracini’s lemma from algebraic geometry. Polyhedral cones are Terracini convex if and only if they are neighborly. More broadly, we derive many families of non-polyhedral Terracini convex cones based on neighborly cones, linear images of cones of positive-semidefinite matrices, and derivative relaxations of Terracini convex hyperbolicity cones. As a demonstration of the utility of our framework in the non-polyhedral case, we give a characterization based on Terracini convexity of the tightness of semidefinite relaxations for certain inverse problems.
Publisher: Springer Science and Business Media LLC
Date: 08-04-2023
DOI: 10.1007/S10107-023-01958-0
Abstract: Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or ‘nice’) which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of the argument, we show that any face of a hyperbolicity cone is a hyperbolicity cone. As a corollary, we show that the intersection of two hyperbolicity cones, not necessarily sharing a common relative interior point, is a hyperbolicity cone.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/120872516
Publisher: IEEE
Date: 12-2014
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 17-10-2023
DOI: 10.1137/22M1500216
Location: United States of America
Location: United States of America
Start Date: 03-2021
End Date: 11-2024
Amount: $395,775.00
Funder: Australian Research Council
View Funded Activity