The Global Optimization of Variational Problems with Discontinuous Solutions

Journal of Global Optimization

Volumn 12, Issue 3, 1998, Pages 225-237

  Rubio, J E ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Calculus of variations; Discontinuous solutions; Global optimization; Loeb measures; Nonstandard analysis; Standard part map

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

CALCULUS OF VARIATION; DISCONTINUOUS SOLUTIONS; LOEB MEASURES; NONSTANDARD ANALYSIS; STANDARD PART MAP;

GLOBAL OPTIMIZATION;

EID: 0342619052     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008213919383     Document Type: Article

References (18)

1. Aldaz, J. M. (1992). A characterization of universal Loeb measurability for completely regular Hausdorff spaces. Canadian Journal of Mathematics, 44: 673-690.
2. Berge, C. (1963). Topological Spaces. Oliver and Boyd.
3. Bressan, A. and Rampazzo, F. (1993). On differential systems with quadratic impulses and their application to Lagrangian mechanics. SIAM Journal on Control and Optimization, 31: 1205-1220.
4. Choquet, G. (1969). Lectures on Analysis. Benjamin.
5. Cutland, N. J., editor (1988). Nonstandard Analysis and its Applications. Cambridge University Press.
6. Henson, C. W. (1979). Analytic sets, Baire sets and the standard part map. Canadian Journal of Mathematics, 31: 663-672.
7. Krotov, V. F. (1961). The principal problem of the calculus of variations for the simplest functional on a set of discontinuous functions. Soviet Mathematics, 2: 231-234.
8. Landers, D. and Rogge, L. (1987). Universal Loeb-measurability of sets and of the standard part map with applications. Transactions of the American Mathematical Society, 304: 229-243.
9. Lawden, D. F. (1959). Discontinuous solutions of variational problems. Journal of the Autralian Mathematical Society, 1: 27-37.
10. Monroe, M. E. (1953). Introduction to Measure and Integration. Addison-Wesley.
11. Oberguggenberger, M. (1992). Multiplication of Distributions and Applications to Partial Differential Equations. Longman.
12. Render, H. (1993). Pushing down Loeb measures. Mathematica Scandinavica, 72: 61-84.
13. Rosenbloom, P. C. (1952). Quelques classes de problèmes éxtremaux. Bulletin de la Societé Mathématique de France, 80: 183-216.
14. Rubio, J. E. (1976). An existence theorem in the calculus of variations. Journal of Optimization Theory and its Applications, 19: 81-87.
15. Rubio, J. E. (1986). Control and Optimisation: The Linear Treatment of Nonlinear Problems. MUP-Wiley.
16. Rubio, J. E. (1994). Optimization and Nonstandard Analysis. Marcel Dekker.
17. Vinter, R. B. and Pereira, F. M. F. L. (1988). A maximum principle for optimal processes with discontinuous trajectories. SIAM Journal on Control and Optimization, 26: 205-229.
18. Young, L. C. (1969). Calculus of Variations and Optimal Control Theory. W. B. Saunders.