On the classical necessary second-order optimality conditions in the presence of equality and inequality constraints

SIAM Journal on Optimization

Volumn 15, Issue 2, 2005, Pages 394-408

  Baccari, Abdeljelil ^a   Trad, Abdelhamid ^b  

^a UNIVERSITY OF TUNIS   (Tunisia)

^b FACULTÉ DES SCIENCES DE TUNIS   (Tunisia)

Author keywords

Constraint qualifications; Necessary conditions; Nonconvex optimization; Pair of quadratic forms

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; LAGRANGE MULTIPLIERS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING;

CONSTRAINTS QUALIFICATIONS; NECESSARY CONDITIONS; NONCONVEX OPTIMIZATION; PAIR OF QUADRATIC FORMS;

CONSTRAINT THEORY;

EID: 18744367538     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S105262340342122X     Document Type: Article

References (11)

1. O. L. MANGASARIAN AND S. FROMOVITZ, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, J. Math. Anal. Appl., 17 (1967), pp. 37-47.
2. M. R. HESTENES, Optimization Theory: The Finite Dimensional Case, Robert E. Krieger Publishing Company, Huntington, NY, 1975.
3. M. S. BAZARAA, H. D. SHERALI, AND C. M. SHETTY, Nonlinear Programming: Theory and Algorithms, John Wiley, New York, 1993.
4. M. ANITESCU, Degenerate nonlinear programming with a quadratic growth condition, SIAM J. Optim., 10 (2000), pp. 1116-1135.
5. J. F. BONNANS AND A. SHAPIRO, Perturbation Analysis of Optimization Problems, Springer-Verlag, Berlin, 2000.
6. J. GAUVIN, A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Math. Program., 12 (1977), pp. 136-138.
7. A. BACCARI, On the classical necessary second-order optimality conditions, J. Optim. Theory Appl., 123 (2004), pp. 213-221.
8. Y. YUAN, On a subproblem of trust region algorithms for constrained optimization, Math. Program., 47 (1990), pp. 53-63.
9. J.-P. CROUZEIX, J.-E. MARTINEZ-LEGAZ, AND A. SEEGER, Un théorème de l'alternative pour des formes quadratiques et quelques extensions, C. R. Acad. Sci. Paris Sér. I Math., 314 (1992), pp. 505-506.
10. J.-E. MARTINEZ-LEGAZ AND A. SEEGER, Yuan's alternative theorem and the maximization of the minimum eigenvalue function, J. Optim. Theory Appl., 82 (1994), pp. 159-167.
11. J.-B. HIRIART-URRUTY AND M. TORKI, Permanently going back and forth between the "quadratic world" and the "convexity world" in optimization, Appl. Math. Optim., 45 (2002), pp. 169-184.