Plenary Speakers and Talks (sorted in presentation order)

 

Dec. 13, 9:10-10:05

    Subspace Techniques for Nonlinear Optimization

    Ya-xiang Yuan (Chinese Academy of Sciences)

    In this talk, we will discuss subspace techniques for nonlinear optimization. The motivations for such an approach are presented, which includes large scale problems and structured problems. Many well known algorithms, such as conjugate gradient methods, limited memory quasi-Newton methods, and null space methods can be viewed as methods based on subspace techniques. We will also give some of our preliminary cosiderations on how to choose subspaces, which is the essential part of such methods.

     

Dec. 13, 10:35-11:30

Optimization and Machine Learning

Kristin P. Bennett (Rensselaer Polytechnic Institute)

In this talk we examine the interplay of optimization and machine learning. Great progress has been made in machine learning by cleverly reducing machine learning problems to convex optimization problems with one or more hyper-parameters. The availability of powerful convex-programming theory and algorithms has enabled a flood of new research in machine learning models and methods. But many of the steps necessary for successful machine learning models fall outside of the convex machine learning paradigm. Thus we now propose framing machine learning problems as Stackelberg games. The resulting bilevel optimization problem allows for fficient systematic search of large numbers of hyper-parameters. We discuss recent progress in solving the resulting bilevel problems and the many interesting optimization challenges that remain. Finally, we investigate the intriguing possibility of novel machine learning models enabled by bilevel programming.

Dec. 13, 11:30-12:25

Computational Methods for a Class of Discrete Valued Optimal Control Problems

Lou Caccetta (Curtin University of Technology)

We consider a general class of optimal control problems where the control functions are assumed piecewise constant and only take on values from a finite discrete set. The aim in such a problem is to find a sequence of discrete control values and a corresponding set of exact switching times (i.e. times where control should switch between the discrete values) such that a given functional representing cost or risk is minimized. Such problems arise in a range of applications. One application is the "Transit Path Problem" where an object such as a robot or vehicle (air, naval, space or land) needs to traverse a specified region (discrete or continuous) between two points in a prescribed time so as to avoid detection. The objective is to find a path for the object which satisfies the time constraints and which minimizes the total risk of detection. The risk function is not simple and depends on a range of factors such as the environment, the types of sensors, the speed, direction and position of the vehicle.

The main difficulty with these problems is that the range of some of the controls is discrete and hence not convex. Since the gradients with respect to the switching time parameters are discontinuous, ordinary gradient based solutions method perform poorly. An additional difficulty is to determine exactly how many switching times are involved in an optimal solution. We address the first difficulty by using the Control Parameterization Enhancing Transform (CPET) and the second difficulty by solving a sequence of problems which are transformed via CPET.

With respect to the transit path problem out strategy involves a two stage approach. The first stage involves a discretization of the problem and the solution of a constrained path problem in a network. The second stage involves the use of an optimal control model and a solution procedure that utilizes the solution obtained from the first stage.

In this talk we present a range of models and solution methods as well as discuss in detail a number of applications.

Professor Louis Caccetta:

Western Australian Centre of Excellence in Industrial Optimisation

Department of Mathematics and Statistics

Curtin University of Technology

GPO Box U1987Perth, Western Australia

email : caccetta@maths.curtin.edu.au

Dec. 14, 9:00-9:55

Generalized Nash Equilibrium Problems

Francisco Facchinei (University of Rome La Sapienza)

The Generalized Nash Equilibrium Problem (GNEP) is a powerful modeling paradigm first introduced in the 1950s in the economic literature. While for a long time the interest in GNEPs has essentially been restricted to economists, in the past fifteen years GNEPs have received an increasing attention and have been used to analyze complex problems arising in several different fields. In this talk I will attempt to review the main results about GNEPs and discuss recent algorithmic advancements.

 

Dec. 14, 10:20-11:15

Evolutionary Multi-Objective Optimization and Decision-Making

Kalyanmoy Deb (Indian Institute of Technology)

Many real-world search and optimization problems are naturally posed as non-linear programming problems having multiple objectives. These problems give rise to a set of Pareto-optimal solutions, any of which cannot be said to be better than the other without further decision-making information. Contrary to conventional methods of finding a single Pareto-optimal solution corresponding a converted single-objective optimization problem, evolutionary multi-objective optimization (EMO) has adequately shown to find a set of Pareto-optimal solutions in a single run. In this talk, the state-of-the-art EMO principles suggested over the past decade will be discussed. Thereafter, recent optimization-cum-decision-making techniques in arriving at a particular solution with the help of decision-making aides are bringing two research groups (EMO and MCDM) together and making the whole effort pragmatic. Some such hybrid techniques will be highlighted with examples. Finally, a newly suggested `innovization' technique in which the EMO approach of finding multiple high-performing solutions are exploited for innovative knowledge extraction will be discussed with case studies.

Brief Bio-Sketch of Kalyanmoy Deb:
Kalyanmoy Deb is currently a Professor of Mechanical Engineering at Indian Institute of Technology Kanpur, India and is the director of Kanpur Genetic Algorithms Laboratory (KanGAL). He is the recipient of the prestigious Shanti Swarup Bhatnagar Prize in Engineering Sciences for the year 2005. He has also received the `Thomson Citation Laureate Award' from Thompson Scientific for having highest number of citations in Computer Science during the past ten years in India. He is a fellow of Indian National Academy of Engineering (INAE), Indian National Academy of Sciences,
and International Society of Genetic and Evolutionary Computation (ISGEC). He has received Fredrick Wilhelm Bessel Research award from Alexander von Humboldt Foundation in 2003. His main research interests are in the area of computational optimization, modeling and design, and evolutionary algorithms. He has written two text books on optimization and more than 190 international journal and conference research papers. He is an associate editor of IEEE Trans. on Evolutionary Computation and an editorial board members of five major journals. More information about his research can be found from http://www.iitk.ac.in/kangal/deb.htm.

Dec. 14, 11:15-12:10

Zonotopes and the LP-Newton Method for Linear Programming

Satoru Fujishige (Kyoto University)

Although linear programming problems can be solved in polynomial time by the ellipsoid method and interior-point algorithms, there still remains a long-standing open problem of devising a strongly polynomial algorithm for linear programming (or of disproving the existence of such an algorithm). The present talk is motivated by an attempt toward solving this problem.

Linear programming problems can be formulated in terms of zonotopes, kinds of greedy polyhedra, on which linear optimization is made easily. We propose a method, called the LP-Newton method, for linear programming that is based on the zonotope formulation of linear programming and the minimum-norm-point algorithm of Philip Wolfe.

Keywords: Zonotope, Linear Programming, Minimum-norm point, Discrete-Newton method


Satoru Fujishige:
Research Institute for Mathematical Sciences
Kyoto University, Kyoto 606-8502, Japan