References
- Ben-Tal A, Zowe J. An unified theory of first and second order conditions for extremum problems in topological vector spaces. Math. Program. Stud. 1982;19:39–77.
- Fiacco AV, McCormick GP. Nonlinear programming: sequential unconstrained minimization techniques. New York (NY): Wiley; 1968.
- Ioffe A. Necessary and sufficient conditions for a local minimum. SIAM J. Control. Optim. 1979;17:245–288.
- Gollan B. Perturbation theory for abstract optimization problems. J. Optim. Theory Appl. 1981;35:417–441.
- Gollan B. On the marginal function in nonlinear programming. Math. Oper. Res. 1984;9:208–221.
- Jittorntrum K. Solution point differentiability without strict complementarity in nonlinear programming. Math. Program. 1984;21:127–138.
- Shapiro A. Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton. Appl. Math. Optim. 1988;18:215–229.
- Bonnans JF, Ioffe AD. Quadratic growth and stability in convex programming problems with multiple solutions. J. Convex Anal. 1995;2:41–57.
- Bonnans JF, Ioffe AD. Second-order sufficiency and quadratic growth for non-isolated minima. Math. Oper. Res. 1995;20:801–817.
- Ioffe AD. On sensitivity analysis of nonlinear programs in Banach spaces: the approach via composite unconstrained optimization. SIAM J. Optim. 1994;4:1–43.
- Shapiro A. Perturbation analysis of optimization problems in Banach spaces. Numer. Funct. Anal. Optim. 1992;13:97–116.
- Studniarski M, Doug E. Ward, Weak sharp minima: characterizations and sufficient conditions. SIAM J. Control Optim. 1999;38:219–236.
- Robinson SM. Generalized equations and their solutions, part ii: applications to nonlinear programming. Math. Program. Stud. 1982;19:200–221.
- Alt W. Stability of solutions for a class of nonlinear cone constrained optimization problems part I: basic theory. Numer. Funct. Anal. Optim. 1989;10:1053–1064.
- Gay DM. Computing optimal locally constrained steps. SIAM J. Sci. Stat. Comput. 1981;2:186–197.
- Sorensen DC. Newton’s method with a model trust region modification. SIAM J. Numer. Anal. 1982;19:409–426.
- Moré JJ. Generalizations of the trust region problem. Optim. Method. Softw. 1993;2:189–209.
- Stern RJ, Wolkowicz H. Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 1995;5:286–313.
- Peng J-M, Yuan Y-X. Optimality conditions for the minimization of a quadratic with two quadratic constraints. SIAM J. Optim. 1997;7:579–594.
- Yang XQ. Second-order global optimality conditions for convex composite optimization. Math. Program. 1998;81:327–347.
- Horn RA, Johnson CR. Matrix analysis, corrected reprint of the 1985 original. Cambridge: Cambridge University Press; 1990.
- Yuan Y. On a subproblem of trust region algorithms for constrained optimization. Math. Program. 1990;47:53–63.
- Martinez-Legaz JE, Seeger A. Yuan’s alternative theorem and the maximization of the minimum eigenvalue function. J. Optim. Theory Appl. 1994;82:159–167.