Apr 11, 2018 Comments Off on Organizers
Organizers
Prof. Andreas Griewank, Universidad Yachay Tech
Prof. Andrea Walther, University of Paderborn
Prof. Siegfried M. Rump, Hamburg University of Technology
Prof. Koichi Kubota, Chuo University
Apr 11, 2018 Comments Off on Participants
Participants
Prof. Paul Barton, MIT Boston
Prof. Bradley Bell, University of Washington
Prof. Francesc Anton Castro, Universidad Yachay Tech
Ms. Olga Ebel, University of Paderborn
Dr. Laurent Hascoet, INRIA
Prof. Xiaolin Huang, Shanghai Jiao Tong University
Prof. Satoru Iwata, University of Tokyo
Prof. Vladik Kreinovich, University of Texas at El Paso
Prof. Fritz Mayer-Lindenberg, Technische Universitat Hamburg
Mr. Taihei Oki, University of Tokyo
Dr. Manuel Radons, Humboldt University of Berlin
Dr. Stephan Schmidt, University of Wuerzburg
Dr. Florian Steinberg, INRIA
Mr. Tom Streubel, Humboldt University of Berlin
Prof. Mizuyo Takamatsu, Chuo University
Dr. Takahito Tanabe, NTT Data Mathematical Systems inc.
Prof. Takashi Tsuchiya, National Graduate Institute for Policy Studies
Dr. Jean Utke, Allstate Insurance Company
Dr. Kathrin Welker, Trier University
(Mr. William Rodolfo Arellano Tamayo,Universidad Yachay Tech)
Apr 11, 2018 Comments Off on Schedule
Schedule
* all talks are about 30min + 10min (Q&A)
24th June (Sunday)
15:00-19:00 Check-in
19:00-21:00 Welcome Banquet
25th June (Monday)
7:30- 9:00 Breakfast
9:00-10:30 Session 1
Introduction (Prof.Andrea Walther)
"Abs-Linearization for Piecewise Smooth Optimization"
Overview on PS,PL
Discussion: Representation and Conversion of PS function
10:30-11:00 Break
11:00-12:00 Session 2
(talk) Ms.Olga Ebel
"Dealing with Optimization Problems
Constrained by Nonlinear Piecewise Smooth PDEs"
Discussion: PL optimization
12:00-13:30 Lunch
13:30-14:00 Group Photo Shooting
14:00-15:30 Session 3
(talk) Prof.Xiaolin Huang
"Parametric and Non-parametric Piecewise
Linear Model and its Optimization"
[(short talk) Prof.Seidel. His arrival time may be around 14:30]
Discussion: PL optimization
15:30-16:00 Break
16:00-18:00 Session 4
(talk) Dr.Jean Utke
"Applying PL optimization to a data science problem"
(new talk) Dr.S.Schmidt
"Non-Smooth Geometric Inverse Problems"
Discussion: Basic PL subroutines
18:00-19:30 Dinner
26th June (Tuesday)
7:30- 9:00 Breakfast
9:00-10:30 Session 1
(talk) Dr.Laurent Hascoet
"Non-smooth tangent differentiation
experiments with Source-Transformation AD tools"
Discussion: Implementation
10:30-11:00 Break
11:00-12:00 Session 2
(new talk) Prof.B.Bell
"CppAD’s Abs-normal Representation"
Discussion: Approximate functions and solvers
12:00-13:30 Lunch
13:30-15:30 Session 3
(talk) Prof.Fritz Mayer-Lindenberg
"Applying automatic functorial substitutions
to simplify programming"
(new talk) Prof. Francesc Anton Castro
"Introduction to Algebraic and Computational Geometry"
Discussion: AD / Interval Implementation
15:30-16:00 Break
16:00-18:00 Session 4
(talk) Dr.Kathrin Welker
"Solution Techniques for Constrained Shape
Optimization Problems in Shape Spaces"
(new talk) Prof.P.Barton
"Lexicographic Derivatives"
Discussion: Approximate functions and solvers
18:00-19:30 Dinner
27th June (Wednesday)
7:30- 9:00 Breakfast
9:00-10:30 Session 1
(new talk) Prof.S.Rump
"Introduction to INTLAB"
(talk) Prof.Vladik Kreinovich
"How Interval Measurement Uncertainty Affects
the Results of Data Processing:
A Calculus-Based Approach to
Computing the Range of a Box"
Discussion: Interval Computation and PL/PS
10:30-11:00 Break
11:00-12:00 Session 2
(talk) Prof.Takashi Tsuchiya
"Chubanov's new polynomial-time algorithm
for linear programming and extensions"
"A Recursive Recomputation Approach to Smoothing in Nonlinear and Bayesian State-Space Modeling"
Discussion: Semi-definite Programming
12:00-13:30 Lunch
13:30-18:00 Excursion
Grate Buddha, Hase Temple
18:15-21:00 Main Banquet
28th June (Thursday)
7:30- 9:00 Breakfast
9:00-10:30 Session 1
(talk) Mr.Taihei Oki
"Index Reduction for Nonlinear
Differential-Algebraic Equations via
Combinatorial Relaxation"
Discussion: PL/PS and DAE/ODE
10:30-11:00 Break
11:00-12:00 Session 2
(new talk) Mr. Tom Streubel
"High Order Taylor-like Expansions of PS functions and their Application to DAEs"
Discussion: (all topics or new topics)
12:00-13:30 Lunch
13:30- Dissmiss
Abstracts.
=====
Prof. Xiaolin Huang, Shanghai Jiao Tong University
"Parametric and Non-parametric Piecewise
Linear Model and its Optimization"
Optimization algorithms are designed for specific formulations,
which are also the basis of modeling piecewise linear systems. Since
the proposal of compact representation, the parametric models of
continuous piecewise linear functions have been insightfully studied
and some models with full representation capability, including our
contributions, have been established. Also, we proposed
non-parametric piecewise linear models by designing specific
kernels. The recent progress of machine learning makes both
parametric and non-parametric piecewise linear models promising to
describe complicated systems. Therefore, it becomes more important
to investigate optimization methods based on the learned
functions. It is also desirable to develop efficient optimization
method to train those piecewise linear models for machine learning.
=====
Dr.Laurent Hascoet, INRIA
"Non-smooth tangent differentiation experiments with
Source-Transformation AD tools"
The research of Andreas Griewank, Andrea Walther, and their
students has shown that Algorithmic Differentiation can be
used to derive tangent models that cope with a certain class
of non-smoothness, through the use of the so-called
Abs-linear form (ALF). These tangent models incorporate some
knowledge of the nearby discontinuities of the
derivatives. These models seem to bring some additional power
to processes that use tangent approximations, such as
simulation, optimization, or solution of differential
equations. The mechanics to derive these special tangent
models may seem at first sightly exotic and remote from
standard tangent linear Algorithmic Differentiation. However,
successful experiments with Adol-C have shown that tangent AD
may be adapted to produce these ALF models. Together with
Krishna Narayanan and following suggestion from Torsten
Bosse, we recently tried a similar adaption on
Source-Transformation AD tools. It appears that very little
development is needed in the AD-tool, be it OpenAD or
Tapenade. Specifically for Tapenade, it appears that no
development at all is needed in the tool itself. Any end-user
can already produce ALF tangent without needing any access to
the tool source. We will detail the required work, which
amounts essentially to hand-writing, once and for all, a
customized derivative of the absolute-value function
(ABS). This is currently less than 40 lines of code.
Building the ALF of a given program introduces one new
variable per run-time execution of the ABS function. As the
number of rows and columns of the constructed extended
Jacobian are both more or less equal to the number of
variables, this extended Jacobian may end up using
unreasonably large memory space for large codes. To overcome
this limitation of the approach, we would like to discuss the
possibility of finding at run-time the "important" ABS calls
that deserve this treatment, and those that don't. We believe
we can base this decision on a notion of distance to the kink
induced by this ABS call, using ideas from the PhD thesis of
Mauricio Araya. We believe that we can also decide at
run-time to forget a previously "important" kink, if we
encounter another one which is closer and therefore more
"important". Thus limiting the number of "active" ABS calls,
we can limit the size of the extended Jacobian to a fixed
number, taking into account only the nearest kinks in the
primal function. We hope to be able to demonstrate this on a
few examples.
=====
Prof. Fritz Mayer-Lindenberg, Technische Universitat Hamburg
"Applying automatic functorial substitutions to simplify programming"
Automatic differentiation will be a special case of such
substitutions (there are more). The talk discusses its
embedding into a particular programming language for
computing with real numbers that attempts to combine
simplicity with the support of difficult targets.
=====
Dr.Kathrin Welker, Trier University
"Solution Techniques for Constrained Shape
Optimization Problems in Shape Spaces"
Shape optimization problems arise frequently in
technological processes which are modelled in the form of
partial differential equations (PDEs) or variational
inequalities (VIs). In many practical circumstances, the
shape under investigation is parametrized by finitely many
parameters, which on the one hand allows the application of
standard optimization approaches, but on the other hand
limits the space of reachable shapes unnecessarily. In this
talk, the theory of shape optimization is connected to the
differential-geometric structure of shape spaces. In
particular, efficient algorithms in terms of shape spaces and
the resulting framework from infinite dimensional Riemannian
geometry are presented. Moreover, VI constrained shape
optimization problems are treated from an analytical and
numerical point of view in order to formulate approaches
aiming at semi-smooth Newton methods on shape vector
bundles. Shape optimization problems constrained by VIs are
very challenging because of the necessity to operate in
inherently non-linear and non-convex shape spaces. In
classical VIs, there is no explicit dependence on the domain,
which adds an unavoidable source of non-linearity and
non-convexity due to the non-linear and non-convex nature of
shape spaces.
=====
Prof.Takashi Tsuchiya, National Graduate Institute for Policy Science
"Chubanov's new polynomial-time algorithm
for linear programming and extensions"
Recently, Chubanov proposed a third polynomial-time algorithm
for linear programming. The problem deals with homogeneous
feasibility problem of a linear program. The algorithm finds
an interior feasible solution of a linear program by
repeating projection and scaling. We extended this algorithm
to symmetric cone programming including SDP and SOCP. In this
talk, we introduce Chubanov's algorithm and discuss further
extensions, seeking for a new direction of conic linear
programming.
=====
Mr.Taihei Oki, University of Tokyo
"Index Reduction for Nonlinear Differential-Algebraic Equations via
Combinatorial Relaxation"
Differential-algebraic equations (DAEs) are widely used for
modeling of dynamical systems. The difficulty in numerically solving
a DAE is measured by its differentiation index. For highly accurate
simulation of dynamical systems, it is important to convert high
index DAEs into low index DAEs. Most of existing simulation software
packages for dynamical systems are equipped with an index reduction
algorithm given by Mattsson and Soederlind. Unfortunately, this
algorithm fails if there are unlucky numerical or symbolic
cancellations. This talk gives a new index reduction algorithm for
nonlinear DAEs. This algorithm modifies a DAE into another DAE to
which Mattsson--Soederlind’s index reduction algorithm is applicable
by iteratively applying the implicit function theorem. Our approach
is based on the combinatorial relaxation approach, which is a
framework to solve a linear algebraic problem by iteratively
relaxing it into an efficiently solvable combinatorial optimization
problem. Though this algorithm heavily uses symbolic manipulations,
we give implementation strategies to overcome the drawback.
=====
Apr 11, 2018 Comments Off on Overview
Overview
Topics
1. Introduction
2. Representation and conversion of PS functions
3. Approximate functions and solvers
4. Basic PL subroutines
5. PS to PL and back
6. Dealing with discontinuities
7. Complexity bounds
8. Interval computation
9. Semi-definite Programming
accommodation fee and full board:
http://shonan.nii.ac.jp/shonan/proposal-submissions/expenses