Who I am

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About me

Since 2008 I am a Research Associate / Adjunct Assistant Professor at the Department of Mathematics and Statistics, University of Calgary. I am a member of Centre for Computational and Discrete Geometry.

I received my PhD in Operations Research from Cornell University in 2005. In 2005-2008 I held a post-doctoral position at the Advanced Optimization Laboratory, McMaster University.

My detailed resume may be found here.



Expertise & Research interests

  • operations research, optimization algorithms and software,

In particular, I am interested in convex optimization – minimizing or maximizing linear functionals over convex subsets of (finite-dimensional real) vector spaces.

Linear Programming (LP) –minimizing a linear functional over a set of finitely many linear inequalities– is, perhaps, one of the most well recognized problems of convex optimization today. In 1975 L. Kantorovich received the Nobel prize in economics for his work in linear programming duality theory; in 1980 and 1984, the subject made the headlines and the front page of New York Times, respectively, with a discovery of a polynomial-time algorithm for LP by L. Khachian, and a discovery of a new practically efficient polynomial-time interior-point method for linear programming by N. Karmarkar. The existence of an algorithm whose run-time is polynomial only in problem dimensions was cited by S. Smale as one of the 18 greatest unsolved problems of the 21st century.

Many numerical methods for convex optimization fall into category of the so-called path-following methods; thus, a better understanding of the underlying paths is essential to developing more efficient optimization algorithms. For instance, any convex optimization problem is, in theory, amenable to Interior-Point Methods (IPM) – a family of particularly efficient numerical algorithms for convex optimization. IPMs typically follow the so-called central path that leads to an optimum.

My thesis work has been primarily dedicated to studying Shrink-Wrapping trajectories for a new class of optimization methods for LP [1], and more generally, convex optimization problems posed over hyperbolicity cones [2]. More recently, I have pursued the study of the curvature of the central path for Linear Programming [3, 4].

  • applications to medicine and health care, optimal radiation therapy design,

In five words, I consider medical applications of mathematics as “math you feel good about”. It is an emerging field where the main impact is yet to come. Applications to oncology and, in particular, radiation therapy treatment design is an important research area that I feel passionate about. The current interdisciplinary research project I am involved in targets a radical advance in the state-of-the-art application of modern convex optimization methods for radiation therapy treatment planning for cancer patients. Extremely high computational demands associated with the optimal radiation therapy treatment planning place this problem in the realm of novel applications for which much more powerful optimization methods, models and numerical software are desperately needed.

The project pursues two main objectives:

a) to minimize the adverse effect of the uncertainties in the radiation therapy treatment planning phase via a combination of image guidance and novel large-scale robust optimization techniques [5],

b) to develop a suitable (convex optimization based) modeling framework for optimal radiotherapy planning that incorporates “dose-volume constraints”, amenable to state-of-the-art computational tools [6].

In 2007 I received Best Novel Use of Mathematics in Technology Transfer MITACS Award for research in optimal and robust radiotherapy design.

  • mathematical programming with applications to computational geometry,

The above mentioned Linear Programming may serve as a perfect example of the intimate relationship between Mathematical Programming / Operations Research and Computational and Discrete Geometry. While LP is one of the most widely used decision making tools of OR, the behavior of many numerical algorithms to solve such problems is studied using the tools and methods of Computational and Discrete Geometry, e.g., one studies the face-lattice of polyhedra to understand the behavior of pivot-type methods.

Recently I became interested in optimization-based bounds for Kissing Numbers. Given an n-dimensional unit sphere centered at the origin, the maximal number of unit spheres that can touch it from the outside, with no mutual overlap, is called the Kissing Number in dimension n. The Kissing Numbers are known only for dimensions 1, 2, 3, 4, 8 and 24. Determining the Kissing Number is a classical problem in geometry and is of particular interest to coding theory (spherical codes).

  • scientific parallel computing and high-performance linear algebra.

Typically convex optimization problems do not admit closed-form analytic solutions and numerical methods have to be used.

Nowadays, one is capable of solving LP problems with millions of variables on a decent computing station. However, for many novel and existing applications there is a compelling need to solve larger and more difficult convex, and not necessarily linear, problems. For instance, the earlier mentioned optimal radiotherapy planning falls within the realm of optimization problems whose computational demands far-exceed the capacities provided by state-of-the-art optimization software.

A dominant computational cost per IPM iteration is attributed to solving nearly dense system of linear equations. Since the dimensions of the system correspond to the dimensions of the underlying optimization problem, the need for high-performance (distributed) linear algebra becomes imminent as the dimensions increase.

We target design and implementation of a modular platform suited for development of high-performance IPM-based solvers. One of the platform design goals is to provide a transparent access to hardware-optimized Basic Linear Algebra Subroutines. For some optimization problem classes we also investigate the use of GP-GPUs.

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Slides from some of my talks

Pathological IPM trajectories

Curvature of the central path

Radiotherapy optimization (with numerical illustration for moment constraints)

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Software projects

Yet Another Solver (YAS) is an open-source object-oriented framework for rapid design of interior-point methods solvers for structured convex optimization problems. Details to be posted.

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List of recently taught courses

Currently I am teaching MATH 211 Linear Methods.

At McMaster University I have taught the following graduate courses:

and held a reading seminar on Interior-Point Methods.

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Contact me

Department of Mathematics and Statistics
Math Science Building , Room 446
University of Calgary
2500 University Drive NW
Calgary, Alberta, Canada T2N 1N4

Phone: 1 (403) 220-4044, Fax: 1 (403) 282-5150

E-mail: yzinchen@ucalgary.ca

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Expertise / Research

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Talks

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Software: YAS

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Recent courses

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Contact me

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Other links

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