Non-existence of perturbed solutions under a second-order sufficient condition
Gerd Wachsmuth
TL;DR
This paper demonstrates that in infinite-dimensional optimization, satisfying the second-order sufficient condition does not guarantee the existence of solutions for perturbed problems, highlighting a limitation in current theoretical assumptions.
Contribution
It provides a counterexample showing that second-order conditions alone are insufficient for solution existence in certain infinite-dimensional problems.
Findings
Counterexample in infinite dimensions
Second-order condition does not ensure solution existence
Highlights limitations of classical optimality conditions
Abstract
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering