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BEGIN:VEVENT
SUMMARY:Tiến-Sơn Phạm (University of Dalat)
DTSTART;VALUE=DATE-TIME:20200603T070000Z
DTEND;VALUE=DATE-TIME:20200603T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/1
DESCRIPTION:Title: Openness\, Hölder metric regularity and Hölder contin
uity properties of semialgebraic set-valued maps\nby Tiến-Sơn Phạm (U
niversity of Dalat) as part of Variational Analysis and Optimisation Webin
ar\n\n\nAbstract\nGiven a semialgebraic set-valued map with closed graph\,
we show that it is Hölder metrically subregular and that the following c
onditions are equivalent:\n\n(i) the map is an open map from its domain in
to its range and the range of is locally closed\;\n\n(ii) the map is Höld
er metrically regular\;\n\n(iii) the inverse map is pseudo-Hölder continu
ous\;\n\n(iv) the inverse map is lower pseudo-Hölder continuous.\n\nAn ap
plication\, via Robinson’s normal map formulation\, leads to the followi
ng result in the context of semialgebraic variational inequalities: if the
solution map (as a map of the parameter vector) is lower semicontinuous t
hen the solution map is finite and pseudo-Holder continuous. In particular
\, we obtain a negative answer to a question mentioned in the paper of Don
tchev and Rockafellar [Characterizations of strong regularity for variatio
nal inequalities over polyhedral convex sets. SIAM J. Optim.\, 4(4):1087
–1105\, 1996]. As a byproduct\, we show that for a (not necessarily semi
algebraic) continuous single-valued map\, the openness and the non-extrema
lity are equivalent. This fact improves the main result of Pühn [Convexit
y and openness with linear rate. J. Math. Anal. Appl.\, 227:382–395\, 19
98]\, which requires the convexity of the map in question.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Théra (University of Limoges)
DTSTART;VALUE=DATE-TIME:20200617T070000Z
DTEND;VALUE=DATE-TIME:20200617T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/2
DESCRIPTION:Title: Old and new results on equilibrium and quasi-equilibriu
m problems\nby Michel Théra (University of Limoges) as part of Variationa
l Analysis and Optimisation Webinar\n\n\nAbstract\nIn this talk I will bri
efly survey some old results which are going back to Ky Fan and Brezis-Nir
emberg and Stampacchia. Then I will give some new results related to the e
xistence of solutions to equilibrium and quasi- equilibrium problems witho
ut any convexity assumption. Coverage includes some equivalences to the Ek
eland variational principle for bifunctions and basic facts about transfer
lower continuity. An application is given to systems of quasi-equilibrium
problems.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco A. López-Cerdá (University of Alicante)
DTSTART;VALUE=DATE-TIME:20200624T070000Z
DTEND;VALUE=DATE-TIME:20200624T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/3
DESCRIPTION:Title: Optimality conditions in convex semi-infinite optimizat
ion. An approach based on the subdifferential of the supremum function\nby
Marco A. López-Cerdá (University of Alicante) as part of Variational An
alysis and Optimisation Webinar\n\n\nAbstract\nWe present a survey on opti
mality conditions (of Fritz-John and KKT-type) for semi-infinite convex op
timization problems. The methodology is based on the use of the subdiffere
ntial of the supremum of the infinite family of constraint functions. Our
approach aims to establish weak constraint qualifications and\, in the las
t step\, to dropp out the usual continuity/closedness assumptions which ar
e standard in the literature. The material in this survey is extracted fr
om the following papers:\n\nR. Correa\, A. Hantoute\, M. A. López\, Weake
r conditions for subdifferential calculus of convex functions. J. Funct. A
nal. 271 (2016)\, 1177-1212.\n\nR. Correa\, A. Hantoute\, M. A. López\, M
oreau-Rockafellar type formulas for the subdifferential of the supremum fu
nction. SIAM J. Optim. 29 (2019)\, 1106-1130.\n\nR. Correa\, A. Hantoute\,
M. A. López\, Valadier-like formulas for the supremum function II: the c
ompactly indexed case. J. Convex Anal. 26 (2019)\, 299-324.\n\nR. Correa\,
A. Hantoute\, M. A. López\, Subdifferential of the supremum via compacti
fication of the index set. To appear in Vietnam J. Math. (2020).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hoa Bui (Curtin University)
DTSTART;VALUE=DATE-TIME:20200708T070000Z
DTEND;VALUE=DATE-TIME:20200708T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/4
DESCRIPTION:Title: Zero Duality Gap Conditions via Abstract Convexity\nby
Hoa Bui (Curtin University) as part of Variational Analysis and Optimisati
on Webinar\n\n\nAbstract\nUsing tools provided by the theory of abstract c
onvexity\, we extend conditions for zero duality gap to the context of non
convex and nonsmooth optimization. Substituting the classical setting\, an
abstract convex function is the upper envelope of a subset of a family of
abstract affine functions (being conventional vertical translations of th
e abstract linear functions). We establish new characterizations of the ze
ro duality gap under no assumptions on the topology on the space of abstra
ct linear functions. Endowing the latter space with the topology of pointw
ise convergence\, we extend several fundamental facts of the conventional
convex analysis. In particular\, we prove that the zero duality gap proper
ty can be stated in terms of an inclusion involving ε-subdifferentials\,
which are shown to possess a sum rule. These conditions are new even in co
nventional convex cases. The Banach-Alaoglu-Bourbaki theorem is extended t
o the space of abstract linear functions. The latter result extends a fact
recently established by Borwein\, Burachik and Yao in the conventional co
nvex case.\n\nThis talk is based on a joint work with Regina Burachik\, Al
ex Kruger and David Yost.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Saunderson (Monash University)
DTSTART;VALUE=DATE-TIME:20200715T070000Z
DTEND;VALUE=DATE-TIME:20200715T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/5
DESCRIPTION:Title: Lifting for simplicity: concise descriptions of convex
sets\nby James Saunderson (Monash University) as part of Variational Analy
sis and Optimisation Webinar\n\n\nAbstract\nThis talk will give a selectiv
e tour through the theory and applications of lifts of convex sets. A lift
of a convex set is a higher-dimensional convex set that projects onto the
original set. Many interesting convex sets have lifts that are dramatical
ly simpler to describe than the original set. Finding such simple lifts ha
s significant algorithmic implications\, particularly for associated optim
ization problems. We will consider both the classical case of polyhedral l
ifts\, which are described by linear inequalities\, as well as spectrahedr
al lifts\, which are defined by linear matrix inequalities. The tour will
include discussion of ways to construct lifts\, ways to find obstructions
to the existence of lifts\, and a number of interesting examples from a va
riety of mathematical contexts. (Based on joint work with H. Fawzi\, J. Go
uveia\, P. Parrilo\, and R. Thomas).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akiko Takeda (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20200729T070000Z
DTEND;VALUE=DATE-TIME:20200729T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/6
DESCRIPTION:Title: Deterministic and Stochastic Gradient Methods for Non-S
mooth Non-Convex Regularized Optimization\nby Akiko Takeda (University of
Tokyo) as part of Variational Analysis and Optimisation Webinar\n\n\nAbst
ract\nOur work focuses on deterministic/stochastic gradient methods for op
timizing a smooth non-convex loss function with a non-smooth non-convex re
gularizer. Research on stochastic gradient methods is quite limited\, and
until recently no non-asymptotic convergence results have been reported. A
fter showing a deterministic approach\, we present simple stochastic gradi
ent algorithms\, for finite-sum and general stochastic optimization proble
ms\, which have superior convergence complexities compared to the current
state-of-the-art. We also compare our algorithms’ performance in practic
e for empirical risk minimization.\n\nThis is based on joint works with T
ianxiang Liu\, Ting Kei Pong and Michael R. Metel.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeni Nurminski (Far Eastern Federal University)
DTSTART;VALUE=DATE-TIME:20200805T070000Z
DTEND;VALUE=DATE-TIME:20200805T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/7
DESCRIPTION:Title: Practical Projection with Applications\nby Evgeni Nurmi
nski (Far Eastern Federal University) as part of Variational Analysis and
Optimisation Webinar\n\n\nAbstract\nProjection of a point on a given set i
s a very common computational operation in an endless number of algorithms
and applications. However\, with exception of simplest sets it by itself
is a nontrivial operation which is often complicated by large dimension\,
computational degeneracy\, nonuniqueness (even for orthogonal projection o
n convex sets in certain situations)\, and so on. This talk aims to presen
t some practical solutions\, i.e. finite algorithms\, for projection on po
lyhedral sets\, among those: simplex\, polytopes\, polyhedron\, finite-gen
erated cones with a certain discussion of “nonlinearities”\, decomposi
tion and parallel computations. We also consider the application of projec
tion operation in linear optimization and epi-projection algorithm for con
vex optimization.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoqi Yang (The Hong Kong Polytechnic University)
DTSTART;VALUE=DATE-TIME:20200812T070000Z
DTEND;VALUE=DATE-TIME:20200812T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/8
DESCRIPTION:Title: On error bound moduli for locally Lipschitz and regular
functions\nby Xiaoqi Yang (The Hong Kong Polytechnic University) as part
of Variational Analysis and Optimisation Webinar\n\n\nAbstract\nWe first i
ntroduce for a closed and convex set two classes of subsets: the near and
far ends relative to a point\, and give some full characterizations for th
ese end sets by virtue of the face theory of closed and convex sets. We pr
ovide some connections between closedness of the far (near) end and the re
lative continuity of the gauge (cogauge) for closed and convex sets. We il
lustrate that the distance from 0 to the outer limiting subdifferential of
the support function of the subdifferential set\, which is essentially th
e distance from 0 to the end set of the subdifferential set\, is an upper
estimate of the local error bound modulus. This upper estimate becomes tig
ht for a convex function under some regularity conditions. We show that th
e distance from 0 to the outer limiting subdifferential set of a lower C^1
function is equal to the local error bound modulus.\n\n\nReferences:\nLi\
, M.H.\, Meng K.W. and Yang X.Q.\, On far and near ends of closed and conv
ex sets. Journal of Convex Analysis. 27 (2020) 407–421.\nLi\, M.H.\, Men
g K.W. and Yang X.Q.\, On error bound moduli for locally Lipschitz and reg
ular functions\, Math. Program. 171 (2018) 463–487.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marián Fabian (Czech Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20200701T070000Z
DTEND;VALUE=DATE-TIME:20200701T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/9
DESCRIPTION:Title: Can Pourciau’s open mapping theorem be derived from C
larke’s inverse mapping theorem?\nby Marián Fabian (Czech Academy of Sc
iences) as part of Variational Analysis and Optimisation Webinar\n\n\nAbst
ract\nWe discuss the possibility of deriving Pourciau’s open mapping the
orem from Clarke’s inverse mapping theorem. These theorems work with the
Clarke generalized Jacobian. In our journey\, we will face several intere
sting phenomena and pitfalls in the world of (just) 2 by 3 matrices.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Stein (Karlsruhe Institute of Technology)
DTSTART;VALUE=DATE-TIME:20200722T070000Z
DTEND;VALUE=DATE-TIME:20200722T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/10
DESCRIPTION:Title: A general branch-and-bound framework for global multiob
jective optimization\nby Oliver Stein (Karlsruhe Institute of Technology)
as part of Variational Analysis and Optimisation Webinar\n\n\nAbstract\nWe
develop a general framework for branch-and-bound methods in multiobjectiv
e optimization. Our focus is on natural generalizations of notions and tec
hniques from the single objective case. In particular\, after the notions
of upper and lower bounds on the globally optimal value from the single ob
jective case have been transferred to upper and lower bounding sets on the
set of nondominated points for multiobjective programs\, we discuss sever
al possibilities for discarding tests. They compare local upper bounds of
the provisional nondominated sets with relaxations of partial upper image
sets\, where the latter can stem from ideal point estimates\, from convex
relaxations\, or from relaxations by a reformulation-linearization techniq
ue. \n \nThe discussion of approximation properties of the provisional
nondominated set leads to the suggestion for a natural selection rule alon
g with a natural termination criterion. Finally we discuss some issues whi
ch do not occur in the single objective case and which impede some desirab
le convergence properties\, thus also motivating a natural generalization
of the convergence concept.\n\nThis is joint work with Gabriele Eichfelder
\, Peter Kirst\, and Laura Meng.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christiane Tammer (Martin Luther University Halle-Wittenberg)
DTSTART;VALUE=DATE-TIME:20200909T070000Z
DTEND;VALUE=DATE-TIME:20200909T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/11
DESCRIPTION:by Christiane Tammer (Martin Luther University Halle-Wittenber
g) as part of Variational Analysis and Optimisation Webinar\n\nAbstract: T
BA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerd Wachsmuth (BTU)
DTSTART;VALUE=DATE-TIME:20200902T070000Z
DTEND;VALUE=DATE-TIME:20200902T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/12
DESCRIPTION:by Gerd Wachsmuth (BTU) as part of Variational Analysis and Op
timisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Regina Burachik (UniSA)
DTSTART;VALUE=DATE-TIME:20200923T070000Z
DTEND;VALUE=DATE-TIME:20200923T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/13
DESCRIPTION:by Regina Burachik (UniSA) as part of Variational Analysis and
Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Price (University of Canterbury)
DTSTART;VALUE=DATE-TIME:20200916T070000Z
DTEND;VALUE=DATE-TIME:20200916T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/14
DESCRIPTION:by Christopher Price (University of Canterbury) as part of Var
iational Analysis and Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yalçın Kaya (UniSA)
DTSTART;VALUE=DATE-TIME:20200930T070000Z
DTEND;VALUE=DATE-TIME:20200930T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/15
DESCRIPTION:by Yalçın Kaya (UniSA) as part of Variational Analysis and O
ptimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hieu Thao Nguyen (TU Delft)
DTSTART;VALUE=DATE-TIME:20200819T070000Z
DTEND;VALUE=DATE-TIME:20200819T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/16
DESCRIPTION:Title: Projection algorithms for phase retrieval with high num
erical aperture\nby Hieu Thao Nguyen (TU Delft) as part of Variational Ana
lysis and Optimisation Webinar\n\n\nAbstract\nWe develop the mathematical
framework in which the class of projection algorithms can be applied to hi
gh numerical aperture (NA) phase retrieval. Within this framework we first
analyze the basic steps of solving this problem by projection algorithms
and establish the closed forms of all the relevant prox-operators. We then
study the geometry of the high-NA phase retrieval problem and the obtaine
d results are subsequently used to establish convergence criteria of proje
ction algorithms. Making use of the vectorial point-spread-function (PSF)
is\, on the one hand\, the key difference between this work and the litera
ture of phase retrieval mathematics which mostly deals with the scalar PSF
. The results of this paper\, on the other hand\, can be viewed as extensi
ons of those concerning projection methods for low-NA phase retrieval. Imp
ortantly\, the improved performance of projection methods over the other c
lasses of phase retrieval algorithms in the low-NA setting now also become
s applicable to the high-NA case. This is demonstrated by the accompanying
numerical results which show that all available solution approaches for h
igh-NA phase retrieval are outperformed by projection methods.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reinier Diaz Millan (Deakin University)
DTSTART;VALUE=DATE-TIME:20201007T060000Z
DTEND;VALUE=DATE-TIME:20201007T070000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/17
DESCRIPTION:by Reinier Diaz Millan (Deakin University) as part of Variatio
nal Analysis and Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jein-Shan Chen (NTNU)
DTSTART;VALUE=DATE-TIME:20200826T070000Z
DTEND;VALUE=DATE-TIME:20200826T080000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/18
DESCRIPTION:Title: Two approaches for absolute value equation by using smo
othing functions\nby Jein-Shan Chen (NTNU) as part of Variational Analysis
and Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Björn Rüffer (University of Newcastle)
DTSTART;VALUE=DATE-TIME:20201014T060000Z
DTEND;VALUE=DATE-TIME:20201014T070000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/19
DESCRIPTION:by Björn Rüffer (University of Newcastle) as part of Variati
onal Analysis and Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilfredo Sosa (UCB)
DTSTART;VALUE=DATE-TIME:20201021T060000Z
DTEND;VALUE=DATE-TIME:20201021T070000Z
DTSTAMP;VALUE=DATE-TIME:20200812T055634Z
UID:VAWebinar/20
DESCRIPTION:Title: On diametrically maximal sets\, maximal premonotone map
s and promonote bifunctions\nby Wilfredo Sosa (UCB) as part of Variational
Analysis and Optimisation Webinar\n\nAbstract: TBA\n
END:VEVENT
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