Workshop on Optimization,
Nonlinear Analysis, Randomness

Saturday, 12th July, 2014
Venue: CARMA, The University of Newcastle


A preliminary programme has been posted below.


There is no registration form, but if you wish to attend, please advise Juliane Turner by email, and include the following information:

  1. if you will attend the get-together (Friday night, 11th July)
  2. if you will come to the dinner (Saturday night, 12th July)
Note that attendess will need to pay for their own dinner on the night.

This one-day workshop, organized by Jonathan Borwein, has no attendance fee but requires registration. The workshop will be preceded by an informal get together on Friday night and followed by a conference dinner on Saturday night. The workshop will be available for remote attendance.

Confirmed Speakers

We are lucky to have the following confirmed speakers. More details will be available soon.
  • David Bailey (LBNL and UCD)
  • Jonathan Borwein (CARMA)
  • Ali Eshragh (CARMA)
  • Alex Kruger (FUA)
    • "Semi-, Sub- and Uniform Regularity of Collections of Sets" [Download PDF]
  • Shuai Liu (RMIT)
    • "A nonmonotone version of bundle trust region method with linear subproblems" [Download PDF]
  • Musa Mammadov (FUA)
    • "Turnpike theorems for convex problems with undiscounted integral functionals" [Download PDF]
  • Asef Nazari (CSIRO, Melbourne)
    • "Some novel algorithms for non-smooth non-convex optimisation problems" [Download PDF]
  • Michael Rose (CARMA)
  • Vera Roshchina (FUA)
  • David Yost (FUA)
  • Jim Zhu (Western Michigan)


The conference will be held in CARMA's rooms, V205 and V206, in the Mathematics Building at the University of Newcastle.

A map of the campus is available here, click on "V Mathematics" in the list below the map to highlight its position.


The preliminary programme is as follows.

8:30 — 9:20Registration and Light Breakfast
9:20 — 9:30Opening remarks by DirectorJon Borwein (CARMA)
9:30 — 10:30Scientific integrity in mathematical finance

The rise of highly mathematical quantitative methods in investment and finance in the past 20 years has exposed the fact that there is a considerable amount of pseudomathematical and pseudoscientific nonsense in the field. As a result, individual investors and fund managers alike are often misled as to the true level of risk in proposed investments. For example, many new investment strategies and exchange-traded funds are promoted by citing "backtest" results -- simulations of a strategy's performance based on historical market data. But what is almost never disclosed is how many different variations of the strategy were explored in developing the strategy. Yet, as myself and three co-authors have shown in our recent paper "Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance," if enough variations of a strategy are tried, almost any desired Sharpe ratio (a standard measure of portfolio performance) can be achieved, due to statistical chance alone. Indeed, it is now thought that statistical overfitting of backtest data may be the principal reason that many new investment strategies and exchange-traded funds, which look good based on published backtests, nonetheless fall flat when actually fielded in the market.

All of this is closely related to the larger issue of reproducibility and professional ethics in the field of scientific research. Just as there is a movement now to require pharmaceutical companies to disclose all results of field tests, good and bad, so researchers and investors should require full disclosure of the extent of backtesting involved in the development of an investment strategy or fund. In a larger sense, we need to ask ourselves why so few are willing to speak out when questionable methodologies and claims are seen in the field of finance (or any other field). As we wrote in our recent paper, "Our silence is consent, making us accomplices in these abuses."

David Bailey (USCD AM keynote)

10:30 — 11:00Random Walks, Polyhedra and Hamiltonian Cycles

In this talk, we introduce a certain polytope, H, induced by a particular discounted Markov decision process corresponding to a given graph G. It has been proved that if the graph G is Hamiltonian, then corresponding to each Hamiltonian cycle in graph G, there exists an extreme point in polytope H, namely, Hamiltonian extreme point. We present our theoretical results on the geometric properties of these extreme points and show that by exploiting them, two new counterpart problems for the Hamiltonian Cycle Problem can be constructed : (1) Searching for one Hamiltonian extreme point in the polytope H; (2) Finding the volume of the polytope H with a desired level of precision. At the end, we conclude this talk with two conjectures derived from these new counterpart problems and provide supporting numerical results.

Ali Ashragh (CARMA)
11:00 — 11:15Coffee
11:15 — 11:45A lower bound theorem for complicated polytopes

We give precise lower bounds on the number of edges of an arbitrary d-dimensional polytope with v vertices, for an interesting range of values of v and d. Previously this problem had only been studied in detail for simplicial polytopes. If time permits, we may indicate the connection with quasilinear mappings on not necessarily locally convex spaces.

David Yost (FUA)
11:45 — 12:15A nonmonotone version of bundle trust region method with linear subproblems

We propose a version of bundle method for minimizing locally Lipschitz and prox-regular functions. A nonmonotone trust region method with box trust region is used so that we solve a linear programming problem in each iteration. We adopt a convexification technique so that adding on a dynamical quadratic term can make the objective function convexifiable. Global convergence is showed in the sense that the iteration sequence converges to a fixed point of the proximal point mapping. This talk is based a PhD project in RMIT.

Leo Shuai (RMIT)
12:15 — 12:45Turnpike theorems for convex problems with undiscounted integral functionals

In this talk the turnpike property is investigated for convex optimal control problems with undiscounted integral functionals. The system is described by a multi-valued mapping having convex graph, and the utility function is assumed to be concave but not necessarily strictly concave. Turnpike theorems are proved under the main assumption that over any given line segment, either the multi-valued mapping is strictly convex or the utility function is strictly concave.

Musa Mamadov (FUA)
12:45 — 1:30Lunch in CARMA
1:30 — 2:30Risk management under a finite investment horizon

Risk management method based on the growth portfolio theory is theoretically superior but often too risky in practice. We will illustrate both in theory and by simulation that the disconnection is due to that in practice investors only invest for a finite time horizon and they need to explicitly address the risk. Incorporate these practical consideration we derive more realistic conservative capital allocation estimate for risk management. Nonsmooth risk functions naturally arise in such problems providing an interesting application example of variational analysis.

This talk is based on collaborative research with Ralph Vince (LSP Partners, LLC) and Marcos Lopez de Prado (Guggenheim Partners).

Jim Zhu (WMU PM keynote)
2:30 — 3:00Semi-, Sub- and Uniform Regularity of collections of Sets

Several local regularity properties of finite collections of sets will be discussed, namely: semiregularity, subregularity and uniform regularity. Metric and dual quantitative characterizations of these properties will be provided as well as their relationships with the corresponding properties of set-valued mappings.

Alex Kruger (FUA)
3:00 — 3:30On the Pataki sandwich theorem

The Pataki sandwich theorem provides (different) necessary and sufficient conditions for a closed convex cone to be facially dual complete (or nice). Examples demonstrate that both conditions are not sharp. We tighten the necessary condition (facial exposedness) further, hence sharpening the sandwich theorem. This is joint work with Levent Tuncel, University of Waterloo.

Vera Roschina (FUA)
3:30 — 3:45Coffee
3:45 — 4:15Some novel algorithms for non-smooth non-convex optimisation problems

In this talk, I present some recent algorithms for non-smooth and non-convex optimisation problems. More specifically, I will demonstrate the secant method, the quasi-secant method, a generalised subgradient method, and an approximate subgradient algorithm for unconstrained problems. The theoretical backgrounds of these methods are explained and some supportive numerical results are demonstrated.

Asef Nazari (CSIRO, Melbourne)
4:15 — 4:45Expectations on Fractal IFS Attractors

We present a measure-theoretic foundation for analysing the expectation of a smooth complex-valued function defined over the attractor of an Iterated Function System (IFS). A Chaos-Game algorithm for numerically computing such expectations naturally follows. This work extends the results of our previous paper (with David Bailey and Richard Crandall), in which such expectations were defined over a restricted class of string-generated Cantor sets, motivated by the desire to analyse neural spatial distributions.

Michael Rose (CARMA)
4:45 — 5:15A very complicated proof of the minimax theorem

The justly celebrated von Neumann minimax theorem has many proofs. Here I reproduce the most complex one I am aware of. This provides a fine didactic example for many courses in convex analysis or functional analysis.

Jon Borwein (CARMA)

Accommodation Suggestions


Sydney Airport to Newcastle

For those arriving at Sydney Airport we recommend taking the train to Newcastle. Take the Airport & East Hills train from Domestic/International Airport Station to Central Station and then the Newcastle and Central Coast train from Central Station to Newcastle Station. From Newcastle Station it is an easy walk to the recommended hotels. For more information and/or to plan your exact trip times see the CityRail website at

Alternatively, there is the Happy Cabby Airport Shuttle Service which you will need to book in advance.

Newcastle Airport to Newcastle

For those arriving at the Newcastle Airport we recommend taking a taxi to Newcastle. The taxi rank is adjacent to the arrivals area of the terminal. Newcastle Taxis can be contacted directly, free-of-charge, on the dedicated taxi phone located in the arrivals end of the terminal.

Alternatively, you can catch the 130 or 131 bus from the Newcastle Airport to the Newcastle Station. From Newcastle Station it is an easy walk to the recommended hotels. For more information and/or to plan your exact trip times see the CityRail website or the Port Stephens Coaches timetables.

Local Transportation in Newcastle

Newcastle Taxis: bookings can be made online or by calling 133 300 within Australia.

Newcastle Buses: the free green 555 Newcastle Shuttle Bus runs every 20 minutes, seven days a week, on a continuous loop around the city centre.

Contact Information

If you have any questions, please contact

Juliane Turner
Telephone: (02) 492 15483
Facimile: (02) 492 16898