Transformation of quadratic forms to perfect squares for broken extremals

Set-Valued Analysis

Volumn 10, Issue 2-3, 2002, Pages 209-232

  Osmolovskii, Nikolai P ^a   Lempio, Frank ^b  

^a MOSCOW STATE UNIVERSITY OF CIVIL ENGINEERING   (Russian Federation)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Broken extremals; Perfect squares; Riccati equation; Sufficient optimality conditions

Indexed keywords

EID: 0141568839     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016588116615     Document Type: Article

References (13)

1. Gelfand, I. M. and Fomin, S. V.: Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ, 1963.
2. Malanowski, K.: Sufficient optimality conditions for optimal control subject to state constraints, SIAM J. Control Optim. 35(1) (1997), 205-227.
3. Maurer H.: First- and second-order sufficient optimality conditions in mathematical programming and optimal control, Math. Programming Study 14 (1981), 42-62.
4. Maurer, H. and Pickenhain, S.: Second-order sufficient conditions for optimal control problems with control-state constraints, J. Optim. Theory Appl. 86 (1995), 649-667.
5. Milyutin, A. A. and Osmolovskii, N. P.: Calculus of Variations and Optimal Control, Amer. Math. Soc., Providence, RI, 1998.
6. Osmolovskii, N. P.: High-order necessary and sufficient conditions for Pontryagin and bounded-strong minima in the optimal control problems, Dokl. Akad. Nauk SSSR 303 (1988), 1052-1056.
7. Osmolovskii, N. P.: Quadratic conditions for nonsingular extremals in optimal control (a theoretical treatment), Russian J. Math. Phys. 2(4) (1994), 487-516.
8. Osmolovskii, N. P.: Quadratic conditions for nonsingular extremals in optimal control (examples), Russian J. Math. Phys. 5(3) (1998), 487-516.
9. Osmolovskii, N. P.: Second-order conditions for broken extremal, In: Proceedings of the Conference Calculus of Variations and Related Topics, Haifa, Israel, 1998.
10. Osmolovskii, N. P. and Lempio, F.: Jacobi-type conditions and Riccati equation for broken extremal, In: R. V. Gamkrelidze (ed.), Modern Mathematics and its Applications 60, 1998, pp. 187-215 (in Russian). English transl. in: J. Math. Sci. 100(5) (2000), 2572-2592.
11. Osmolovskii, N. P. and Lempio, F.: Jacobi-type conditions and Riccati equation for broken extremal, In: R. V. Gamkrelidze (ed.), Modern Mathematics and its Applications 60, 1998, pp. 187-215 (in Russian). English transl. in: J. Math. Sci. 100(5) (2000), 2572-2592.
12. Reid, W. T.: Riccati Differential Equations, Academic Press, New York, 1972.
13. Zeidan, V.: The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency, SIAM J. Control Optim. 32(5) (1994), 1297-1321.