Abstract
The scaled gradient projection (SGP) methods introduce in [3] and subsequently modified and extended in [5,6,7,10,11,12] are effective for specially structured constrained minimization problems
in simple closed convex feasible sets,
where u is a normed vector space, J is a smooth real-valued objective function and g is a smooth function from u to a normed vector space V with a partial order relation, ≤.These methods are particularly useful for optimal control problems with constraints on the range of admissible control sequences or functions. In problems of this sort, g is typically “separable”, Ω amounts to a Cartesian product of elementary closed convex sets U with dim U ≪ dim u ≤ ∞ , and projection into Ω, decomposes into many readily computed projections into U. Furthermore, structure inherent in J makes it possible to compute Newtonian convergence-accelerating transformations of ∇J(u) efficiently in O(k) floating point operations, where k is the number of stages in a discrete-time optimal control problem, or the number of mesh subintervals in a finite-difference approximation to a continuous-time optimal control problem.
Keywords
- Optimal Control Problem
- Gradient Projection Method
- Constrain Minimization Problem
- Normed Vector Space
- Floating Point Operation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Dunn, J.C. (1991). Scaled Gradient Projection Methods for Optimal Control Problems and Other Structured Nonlinear Programs. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_32
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DOI: https://doi.org/10.1007/978-1-4612-0439-8_32
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