Professor Andrew Eberhard is Deputy Head – Mathematics and Statistics at RMIT University, Program Leader Platform Technology Research Institute (Information and Networks) and the Director of the Australian Mathematical Sciences Institute, 2016 Summer School.
Professor Eberhard is an expert in the study of convergence and the approximation of convex and other nonlinear functions. This includes the study of the effect approximations have on the differential and duality properties of optimization problems based on these functions. I have a broad interest in optimization theory and algorithms working in both continuous, nonsmooth optimization as well as integer programming.
He has applied theory that he has developed to many applications including control theory, nonsmooth optimality conditions, the theory of viscosity solutions of elliptic partial differential equations and the theory of optimization algorithms of various types. He has also used these methods to study the best fit problem for utility functions based on observations of a consumer's revealed preferences.
Professor Eberhard has also pioneered the use of various geometric structures from generalized convexity in nonsmooth analysis. Such methods have also proven very useful in the development of theories in second order nonsmooth analysis and its application to optimization.
He has experience in the application of duality theory to the reformulation and solution of optimization problems. Recently these techniques have provided a theory to explain and improve the Feasibility Pump for Mixed Integer Programming. Techniques for convex and functional analysis have also been exploited to great effect in obtaining qualitative and quantitative information for control design and signal processing problems. Professor Eberhard has an interest in monotone operator theory and convex analysis.
Professor Eberhard is Director of the Australian Mathematical Sciences Institute, 2016 Summer School.
- Doctor of Philosophy (Applied Mathematics), Adelaide University, 1987
Professional interests and links to industry
- Member of Australian Mathematics Society
- Member of Mathematical Optimization Society
- Member of Australian Society for Operations Research (ASOR)
- Member of Society for Industrial and Applied Mathematics (SIAM)
- Member of SIAM and of the special interest group on discrete mathematics
- Member of Pacific Optimization Research Activity Group (POP)
- Associate Editor the electronic Newsletter `Optimization Research Bridge' (of POP) from 2001 to 2008
- Member of Working Group on Generalized Convexity (WGGC)
- Associate Editor for the ANZIAM Journal
- Associate Editor for the The Australian Journal of Mathematical Analysis and Applications (ANJMAA)
- Associate Editor for the International Transactions in Operations Research (ITORS)
- Executive member of SigmaOpt, the ANZIAM special interest group on optimisation.
- Access Grid Room Coordinator at RMIT
- Chair of the Access Grid Steering Committee of the Australian Mathematical Sciences Institute (AMSI)
- Member of the Research and Higher Degrees Committee of AMSI.
- Reviewer for AMS Mathematical Reviews
Accomplishments and achievements
- Invited speaker at the Australian-Chinese workshops on optimisation held at Ballarat University in the years 2004, 2009, 2010 and 2013
- Program Leader Platform Technologies Research Institute (Information and Networks) 2012 – present
- Plenary Speaker at ANZIAM 2012 in Warrnambool.
- Deputy Director of the Australian Mathematical Sciences Institute from 2010-2012
- Held Visiting Professor's position at the Universite of Perpignan, France 2010.
- Invited to teach at the 2004 and 2006 - AMSI summer schools.
- Visiting Professor, Dalhousie University, Halifax, Nova Scotia, Canada in 2005.
- In 1999 he held the position of Visiting Professor at the Universite Blaise Pascal, in Clermont-Ferrand, France.
- Invited to speak at the "Nonlinear Dynamics and Optimization" session at the joint meeting of the American and Australian Mathematical Societies held in Melbourne during 12th-16th July 1999.
- Liu, S.,Eberhard, A.,Luo, Y. (2020). The U -Lagrangian, Fast Track, and Partial Smoothness of a Prox-regular Function In: Set-Valued and Variational Analysis, 28, 369 - 394
- Eberhard, A.,Mordukhovich, B.,Rieger, J. (2020). Explicit Formula for Preimages of Relaxed One-Sided Lipschitz Mappings with Negative Lipschitz Constants: A Geometric Approach In: Journal of Optimization Theory and Applications, 185, 34 - 43
- Eberhard, A. (2020). Orbital Geometry and Group Majorisation in Optimisation In: Vietnam Journal of Mathematics, 48, 537 - 567
- Eberhard, A.,Roshchina, V.,Sang, T. (2019). Outer limits of subdifferentials for min-max type functions In: Optimization, 68, 1391 - 1409
- Pinheiro De Oliveira, F.,Christiansen, J.,Dandurand, B.,Eberhard, A. (2019). Combining penalty-based and Gauss-Seidel methods for solving stochastic mixed-integer problems In: International Transactions in Operational Research, 27, 494 - 524
- Dontchev, A.,Eberhard, A.,Rockafellar, R. (2019). Radius theorems for monotone mappings In: Ste-Valued and Variational Analysis, 27, 605 - 621
- Boland, N.,Christiansen, J.,Dandurand, B.,Eberhard, A.,Oliveira, F. (2019). A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems In: Mathematical Programming, Series A, 175, 503 - 536
- Eberhard, A.,Luo, Y.,Liu, S. (2019). On partial smoothness, tilt stability and the VU-decomposition In: Mathematical Programming, 175, 155 - 196
- Alrabeeah, M.,Munapo, E.,Alhasani, A.,Kumar, S.,Eberhard, A. (2019). Computational enhancement in the application of the branch and bound method for linear integer programs and related models In: International Journal of Mathematical, Engineering and Management Sciences, 4, 1140 - 1153
- Al-Rabeeah, M.,Kumar, S.,Al-Hasani, A.,Munapo, E.,Eberhard, A. (2019). Bi-objective integer programming analysis based on the characteristic equation In: International Journal of Systems Assurance Engineering and Management, , 1 - 8
- Switching Dynamics Approach for Distributed Global Optimisation. Funded by: ARC Discovery Projects 2020 from (2020 to 2023)
- Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Funded by: ARC Discovery Grant 2014 from (2014 to 2019)
- Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Administered by The University of Newcastle.. Funded by: Australian Research Council Discovery via The University of Newcastle Grant 2012 from (2012 to 2014)
- New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Administerd by The University of Newcastle.. Funded by: ARC Discovery Projects via other University Grant pre-2014 from (2009 to 2011)
- Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies.. Funded by: ARC Discovery 2006 from (2006 to 2009)
10 PhD Completions and 2 Masters by Research Completions4 PhD Current Supervisions