# Minima in control problems with constraints

Gianna Stefani; PierLuigi Zezza

Banach Center Publications (1995)

- Volume: 32, Issue: 1, page 361-378
- ISSN: 0137-6934

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topStefani, Gianna, and Zezza, PierLuigi. "Minima in control problems with constraints." Banach Center Publications 32.1 (1995): 361-378. <http://eudml.org/doc/262775>.

@article{Stefani1995,

abstract = {This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated linear-quadratic problem and then by giving a conjugate point theory for this linear quadratic problem with constraints.},

author = {Stefani, Gianna, Zezza, PierLuigi},

journal = {Banach Center Publications},

keywords = {state-control constraint; necessary; second order conditions; conjugate points; optimal control; sufficient conditions; optimality conditions; conjugate point; weak local minimum; endpoint equality constraints; mixed control-state equality constraints},

language = {eng},

number = {1},

pages = {361-378},

title = {Minima in control problems with constraints},

url = {http://eudml.org/doc/262775},

volume = {32},

year = {1995},

}

TY - JOUR

AU - Stefani, Gianna

AU - Zezza, PierLuigi

TI - Minima in control problems with constraints

JO - Banach Center Publications

PY - 1995

VL - 32

IS - 1

SP - 361

EP - 378

AB - This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated linear-quadratic problem and then by giving a conjugate point theory for this linear quadratic problem with constraints.

LA - eng

KW - state-control constraint; necessary; second order conditions; conjugate points; optimal control; sufficient conditions; optimality conditions; conjugate point; weak local minimum; endpoint equality constraints; mixed control-state equality constraints

UR - http://eudml.org/doc/262775

ER -

## References

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- [27] P. Zezza, The Jacobi condition for elliptic forms in Hilbert spaces, J. Optim. Theory Appl. 76 (1993), 357-380. Zbl0798.49027

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