Good and Bad Optimization Models: Insights from Rockafellians
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Authors
Royset, Johannes O.
Subjects
optimization models
Rockafellian functions
sensitivity analysis
optimality conditions
normal cones
subgradients
Rockafellian relaxation
Rockafellian functions
sensitivity analysis
optimality conditions
normal cones
subgradients
Rockafellian relaxation
Advisors
Date of Issue
2021-06-29
Date
Publisher
ArXiv
Language
Abstract
A basic requirement for a mathematical model is often that its solution (output) shouldn’t
change much if the model’s parameters (input) are perturbed. This is important because the exact values
of parameters may not be known and one would like to avoid being misled by an output obtained using
incorrect values. Thus, it’s rarely enough to address an application by formulating a model, solving the
resulting optimization problem and presenting the solution as the answer. One would need to confirm
that the model is suitable, i.e., “good,” and this can, at least in part, be achieved by considering a
family of optimization problems constructed by perturbing parameters as quantified by a Rockafellian
function. The resulting sensitivity analysis uncovers troubling situations with unstable solutions, which
we referred to as “bad” models, and indicates better model formulations. Embedding an actual problem
of interest within a family of problems via Rockafellians is also a primary path to optimality conditions
as well as computationally attractive, alternative problems, which under ideal circumstances, and when
properly tuned, may even furnish the minimum value of the actual problem. The tuning of these
alternative problems turns out to be intimately tied to finding multipliers in optimality conditions and
thus emerges as a main component of several optimization algorithms. In fact, the tuning amounts to
solving certain dual optimization problems. In this tutorial, we’ll discuss the opportunities and insights
afforded by Rockafellians.
Type
Preprint
Description
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Office of Naval Research
Air Force Office of Scientific Research
Air Force Office of Scientific Research
Funding
MIPR F4FGA00350G004
MIPR N0001421WX01496
MIPR N0001421WX01496
Format
36 p.
Citation
Royset, Johannes O. "Good and Bad Optimization Models: Insights from Rockafellians." arXiv preprint arXiv:2105.06073 (2021).
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.