An Invariant Set Approach for Optimization on Integrable Manifolds
arXiv:1905.01626h-index: 8
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This work provides a new theoretical framework for solving constrained optimization problems on manifolds, potentially benefiting fields like control systems and numerical integration.
The paper proposes an algorithm that uses invariant set theory to transform constrained optimization problems on integrable manifolds into unconstrained ones, enabling simpler solution methods.
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an algorithm to solve a class of constrained optimization problems as unconstrained problems.