BEGIN:VCALENDAR
PRODID:-//Ben Fortuna//iCal4j 1.0//EN
VERSION:2.0
CALSCALE:GREGORIAN
X-WR-CALNAME:Seminar\, Optimization and systems theory
BEGIN:VEVENT
DTSTAMP:20230329T204411Z
SUMMARY:Nick Sahinidis\, Title: Global black-box optimization
DESCRIPTION:Abstract
\n
\nThis talk presents recent theoretical\, algorithmic\, and methodologica
l advances for black-box optimization problems for which optimization mu
st be performed in the absence of an algebraic formulation\, i.e.\, by u
tilizing only data originating from simulations or experiments. We inves
tigate the relative merits of optimizing surrogate models based on gener
alized linear models and deep learning. Additionally\, we present new op
timization algorithms for direct data-driven optimization. Our approach
combines model-based search with a dynamic domain partition strategy tha
t guarantees convergence to a global optimum. Equipped with a clustering
algorithm for balancing global and local search\, the proposed approach
outperforms existing derivative-free optimization algorithms on a large
collection of problems.
\n
LOCATION:seminar room 3418
DTSTART:20220923T130000Z
DTEND:20220923T140000Z
UID:98fa7ffc-5de5-4a6e-b3ed-f8a4d462aaa7
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230329T204411Z
SUMMARY:Finding feasible operation modes for power distribution systems b
y discrete adjustments in distributional robust optimization
DESCRIPTION:Abstract: In recent years the amount of distributed generator
s (DG)\, such as local wind farms or solar cells\, in power distribution
systems (PDS) has increased rapidly. However\, the power generation of
these DGs is affected by uncertainties\, e.g. stemming from weather cond
itions. These uncertainties may threaten the grid safety and thus smart
inverters were developed to stabilize the voltage.
\nIn this talk we propose a mathematical framework to optimize the operat
ion mode of the smart inverters. The framework boils down to a distribut
ional robust optimization problem\, where it is possible to adjust some
of the variables to the realized uncertainty in the capacity of the DGs.
Particularly\, one obtains a three-level optimization problem with disc
rete decisions on the lowest level. In order to address this problem\, w
e aim to develop a branch-and-bound algorithm\, that provides feasible s
olutions for this very challenging problem.
\n
\n
LOCATION:Seminar room 3721
DTSTART:20221021T123000Z
DTEND:20221021T123000Z
UID:c5cbe13d-29d6-4fc3-8b0d-6739c849e57c
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230329T204411Z
SUMMARY:Convexification techniques for signomial functions in mixed-integ
er nonlinear optimization
DESCRIPTION:The topic of this presentation is how to utilize so-called li
fting exponential and power transformations in combination with lineariz
ation techniques to solve nonconvex mixed integer nonlinear optimization
(also called mixed-integer nonlinear programming – MINLP) problems cont
aining signomial functions. Signomial functions are sums of terms\, wher
e each term is a product of power functions. This function class is quit
e general and contain common nonconvexities in optimization problems suc
h as bilinear and trilinear terms.
\n
\n
LOCATION:3721
DTSTART:20221125T100000Z
DTEND:20221125T110000Z
UID:11259e87-2666-4265-b91d-5997d573abd6
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230329T204411Z
SUMMARY:MATHEMATICAL THEORY OF CONTINUOUS NONLINEAR OPTIMAL SET PARTITION
(OPS) PROBLEMS WITH ARRANGEMENT OF SUBSET CENTERS
DESCRIPTION:Abstract:
\nMathematical theory of continuous nonlinear problems of optimal partiti
on of a set Ω in an n-measurable Euclidean space into disjoint subsets w
ith arrangement of their centers is proposed.
\n
\nMathematical formulations of continuous nonlinear OPS problems with the
arrangement of the centers of subsets under equality and inequality con
straints or without constraints are formulated for cases of convex or co
ncave nonlinear parts of the objective functional. The solution methods
are substantiated for these problems. They are based on passing from the
original nonlinear infinite-dimensional optimization problem through th
e Lagrangian functional and with application of the Kuhn–Tucker theory t
o the dual finite-dimensional problem with nonsmooth objective functiona
l\, and with the simultaneous obtaining of the analytical relations of d
irect and dual variables while solving the auxiliary operator equation w
ith parameters. For solving the obtained nonsmooth dual task an objecti
ve functional is minimized by the method of generalized pseudogradients
with space dilatation close to the Shor r-algorithm or its modifications
.
\n
\nThe possibility of transferring and applying the theory of continuous n
onlinear OPS problems with arrangement of subset centers to the case of
corresponding continuous nonlinear OPS problems with fixed subset center
s is shown.
\n
\nModels of some applied infinite-dimensional problems of the arrangement
of enterprises with simultaneous partition of a given region\, continuo
usly filled with customers\, into domains of customers are developed. Ea
ch domain is serviced by one enterprise in order to minimize transportat
ion and industrial costs. The customers may be telephone/ Internet subsc
ribers\, students\, voters\, points of an irrigated territory\, patients
to be diagnosed\, etc. The NOPS system (which is a software implementat
ion of all the above algorithms) was created and used for solving such p
roblems both with the arrangement of the centers of subsets and with fix
ed centers of subsets. A comparative analysis of the results has shown t
hat the methods that provide the possibility of center arrangement are m
ore effective in optimizing the partitioning quality criterion.
\n
LOCATION:3721
DTSTART:20221202T090000Z
DTEND:20221202T094500Z
UID:c1548733-34db-49a5-82a3-57062e998830
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20230329T204411Z
SUMMARY:Title: Randomized Assortment Optimization
DESCRIPTION:Abstract: When a firm selects an assortment of products to of
fer to customers\, it uses a choice model to anticipate their probabilit
y of purchasing each product. In practice\, the estimation of these mode
ls is subject to statistical errors\, which may lead to significantly su
boptimal assortment decisions. Recent work has addressed this issue usin
g robust optimization\, where the true parameter values are assumed unkn
own and the firm chooses an assortment that maximizes its worst-case exp
ected revenues over an uncertainty set of likely parameter values\, thus
mitigating estimation errors. In this talk\, we introduce the concept o
f randomization into the robust assortment optimization literature. We s
how that the standard approach of deterministically selecting a single a
ssortment to offer is not always optimal in the robust assortment optimi
zation problem. Instead\, the firm can improve its worst-case expected r
evenues by selecting an assortment randomly according to a prudently des
igned probability distribution. We demonstrate this potential benefit of
randomization both theoretically in an abstract problem formulation as
well as empirically across three popular choice models: the multinomial
logit model\, the Markov chain model\, and the preference ranking model.
We show how an optimal randomization strategy can be determined exactly
and heuristically. Besides the superior in-sample performance of random
ized assortments\, we demonstrate improved out-of-sample performance in
a data- driven setting that combines estimation with optimization. Our r
esults suggest that more general versions of the assortment optimization
problem—incorporating business constraints\, more flexible choice model
s and/or more general uncertainty sets—tend to be more receptive to the
benefits of randomization.
\n
\n
LOCATION:3721
DTSTART:20221202T100000Z
DTEND:20221202T110000Z
UID:71752af3-273a-48b0-9430-69ae53ffd4f3
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