### A Full Rank Condition for Continuous-Time Optimization Problems with Equality and Inequality Constraints

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

R. Bellman, “Bottleneck problems and dynamic programming,” in Proceedings of the National Academy of Sciences, vol. 39, pp. 947–951, National Acad. Sciences, 1953.

R. Bellman, Dynamic Programming. Princeton University Press, 1957.

G. Zalmai, “Optimality conditions and Lagrangian duality in continuous-time nonlinear programming,” Journal of mathematical analysis and applications, vol. 109, no. 2, pp. 426–452, 1985.

M. A. Hanson and B. Mond, “A class of continuous convex programming problems,” Journal of Mathematical Analysis and Applications, vol. 22, no. 2, pp. 427–437, 1968.

N. Levinson, “A class of continuous linear programming problems,” Journal of Mathematical Analysis and Applications, vol. 16, no. 1, pp. 73–83, 1966.

W. H. Farr and M. A. Hanson, “Continuous time programming with nonlinear time delayed constraints,” Journal of Mathematical Analysis and Applications, vol. 46, no. 1, pp. 41–61, 1974.

W. H. Farr and M. A. Hanson, “Continuous time programming with nonlinear constraints,” Journal of Mathematical Analysis and Applications, vol. 45, no. 1,

pp. 96–115, 1974.

T. W. Reiland and M. A. Hanson, “Generalized kuhn-tucker conditions and duality for continuous nonlinear programming problems,” Journal of Mathematical Analysis and Applications, vol. 74, no. 2, pp. 578–598, 1980.

J. Abrham and R. N. Buie, “Kuhn-tucker conditions and duality in continuous programming,” Utilitas Math, vol. 16, no. 1, pp. 15–37, 1979.

T. W. Reiland, “Optimality conditions and duality in continuous programming i. convex programs and a theorem of the alternative,” Journal of Mathematical Analysis and Applications, vol. 77, no. 1, pp. 297–325, 1980.

W. I. Zangwill, Nonlinear programming: a unified approach. Prentice-Hall, 1969.

B. D. Craven and J. J. Koliha, “Generalizations of Farkas theorem,” SIAM Journal on Mathematical Analysis, vol. 8, no. 6, pp. 983–997, 1977.

A. J. V. Brandão, M. A. Rojas Medar, and G. N. Silva, “Nonsmooth continuoustime optimization problems: necessary conditions,” Computers and Mathematics with Applications, vol. 41, no. 12, pp. 1477–1486, 2001.

M. A. Rojas Medar, A. J. Brandao, and G. N. Silva, “Nonsmooth continuous time optimization problems: sufficient conditions,” Journal of Mathematical Analysis and Applications, vol. 227, no. 2, pp. 305–318, 1998.

V. De Oliveira and M. Rojas-Medar, “Continuous-time optimization problems involving invex functions,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 1320–1334, 2007.

D. Martin, “The essence of invexity,” Journal of optimization Theory and Applications, vol. 47, no. 1, pp. 65–76, 1985.

V. Oliveira, M. A. Rojas Medar, and A. J. V. Brandão, “A note on KKT-invexity in nonsmooth continuous-time optimization,” Proyecciones (Antofagasta), vol. 26, no. 3, pp. 269–279, 2007.

V. A. De Oliveira and M. A. Rojas-Medar, “Continuous-time multiobjective optimization problems via invexity,” Abstract and Applied Analysis, vol. 2007, no. 1, p. 11, 2007.

V. A. de Oliveira, “Vector continuous-time programming without differentiability,” Journal of Computational and Applied Mathematics, vol. 234, no. 3, pp. 924–933, 2010.

M. R. de Pinho and R. Vinter, “Necessary conditions for optimal control problems involving nonlinear differential algebraic equations,” Journal of Mathematical Analysis and Applications, vol. 212, no. 2, pp. 493–516, 1997.

G. Zalmai, “Proper efficiency principles and duality models for a class of continuous-time multiobjective fractional programming problems with operator constraints,” Journal of Statistics and Management Systems, vol. 1, no. 1, pp. 11–59, 1998.

L. A. Lusternik and V. J. Sobolev, Elements of Functional Analysis. Frederick Ungar, New York, 1961.

L. N. Trefethen and D. Bau III, Numerical linear algebra. Siam, 1997.

W. Rudin, Principles of Mathematical Analysis 3rd Edition. McGraw-Hill, New York, 1976.

DOI: https://doi.org/10.5540/tema.2019.020.01.15

#### Article Metrics

_{Metrics powered by PLOS ALM}

### Refbacks

- There are currently no refbacks.

**TEMA - Trends in Applied and Computational Mathematics**

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

ISSN: 1677-1966 (print version), 2179-8451 (online version)

Indexed in: