January, 2017

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Talk by Hoa Bui on 3 February


Speaker: Ms Hoa Thi Bui
Federation University Australia

Title: Quasiconvexity and robust quasiconvexity

Date and time: Friday, 3 February 2017, 4:00-5:00pm.
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: A quasiconvex function, or a level-convex function, is a function whose sublevel sets are convex. And, the class of functions which are stable in term of the quasiconvexity under the sufficiently small linear perturbations is called robustly quasiconvex functions. This aims to give a concept of generalised convexity, at which many important properties of the convexity still hold under a relatively small perturbation. Then, the quasiconvexity and robust quasiconvexity of lower semicontinuous functions are characterized by means of Fréchet and limiting subdifferentials.

Bio: Hoa Thi Bui has recently arrived from Vietnam to take up a PhD position at Federation University. She comes from Quang Ngai, Vietnam and up until recent graduation, studied Mathematics at Ho Chi Minh City, University of Pedagogy, Vietnam.

Her PhD Supervisors are Prof. Alex Kruger and Prof. David Yost.

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Talk by Melvyn Sim on 23 January


Speaker: Prof. Melvyn Sim
National University of Singapore

Title: Distributionally Robust Optimization

Date and time: Monday 23 January 2017, 3:00pm.
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Hence, depending on the ambiguity set, the resulting framework is either a linear optimization problem or a second-order conic optimization problem (SOCP), which can be solved efficiently by general purpose commercial grade solvers. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high quality solutions for addressing a medical appointment scheduling problem and a multiperiod inventory control problem.

Bio: Prof. Melvyn Sim is the Head of Department and Provost’s Chair Professor at the Department of Decisions Sciences, NUS Business school. His research interests fall broadly under the categories of decision making and optimization under uncertainty with applications ranging from finance, supply chain management, healthcare to engineered systems. He serves as an associate editor for Operations Research, Management Science and Mathematical Programming Computations.

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Talk by Pierluigi Cesana on 27 January


Speaker: Dr Pierluigi Cesana
Senior Research Fellow
Department of Mathematics and Statistics
La Trobe University

Title: Smart membranes that do not wrinkle

Date and time: Friday, 27 January 2017, 4:00-5:00pm.
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: For liquid crystal elastomers in the thin film limit, an interplay of material and structural non-linearities is observed. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and oscillations of the local optical axis that one expects in elastic liquid crystals. In this talk we present an energy-optimization approach based on relaxation and Gamma-convergence to describe the effective energy density of thin membranes of liquid crystal elastomers by providing a detailed characterization of the fine-scale features. Mathematically, this is an intricate minimization problem with many non-linear and non-convex constraints (such as kinematics, geometrical confinement, optical anisotropy). Importantly, we show existence of a regime where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling. This may act as a mechanism preventing formation of wrinkles in membranes under complex boundary conditions. Based on this feature, current work is being carried on on the design of programmable membranes and wrinkle-free inflatable reflectors with potential applications in satellites and space probes.

Bio: I graduated at SISSA, Italy in 2009 with a PhD in calculus of variations and elasticity theory. I worked as a postdoc in the US across Caltech and Los Alamos Nat Lab till 2013 before moving to the Mathematical Institute at Oxford and as of 2015 am based at La Trobe. In my research I have been adopting energy-minimization approaches in materials science with a special focus on elastic-liquid crystals (artificial lenses and muscles) and metallurgy (pattern formation and topological defects in Shape-Memory Alloys). More recently I have been adopting tools from probability theory to study self-organization and criticality in the microstructure of elastic crystals.

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Talk by Asen Dontchev on 20 January


The first RMITOpt talk next year will be on Friday 20 January, 12:30pm, by Prof. Asen Dontchev.

Speaker: Prof. Asen L. Dontchev, Mathematical Reviews and the University of Michigan
Title: Strong Metric Subregularity
Date and time: Friday, 20 January 2017, 12:30-13:30pm
Location: 8.9.66 (RMIT Access grid room)

Abstract: Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various (equivalent) definitions for more than two decades, it has attracted much less attention than its older "siblings", the metric regularity and the strong metric regularity.
In this talk I will try to show that the strong metric subregularity shares the main features of these two most popular regularity properties and is not less instrumental in applications. In particular, it obeys the inverse function theorem paradigm also for nonsmooth perturbations.
A sufficient condition for strong metric subregularity is established in terms of surjectivity of the Fréchet coderivative will be presented, and it will be shown by a counterexample that surjectivity of the limiting coderivative is not a sufficient condition for this property, in general. Then various versions of Newton's method for solving variational inequalities will be considered including inexact and semismooth methods. A characterization of the strong metric subregularity of the KKT mapping will be demonstrated, as well as a radius theorem for the optimality mapping of a nonlinear programming problem. Finally, an error estimate is derived for a discrete approximation in optimal control under strong metric subregularity of the mapping involved in the Pontryagin principle.

Bio: Asen got both his MS and PhD degrees at Warsaw Polytechnics, Poland, in then famous Polish school in control. Then he moved to his home country, Bulgaria, where is received his DSc dgree, went through the ranks and became Full Professor at the Institute of Mathematics, Bulgarian Acad. of Sciences. In early 90s he accepted the position of Associate Editor at Mathematical Review in Ann Arbor, where he also has taught at the University of Michigan; he is currently appointed there as a Research Scientist. His research interests cover several areas in control, optimization, and applied analysis.

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