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Zbl 0711.90062
Yuan, Y.
On a subproblem of trust region algorithms for constrained optimization. (English)
[J] Math. Program., Ser. A 47, No.1, 53-63 (1990). ISSN 0025-5610; ISSN 1436-4646/e

The author studies a subproblem which appears in some trust region algorithms for constrained optimization, where the original problem is to minimize a nonlinear function subject to equality constraints. It is the minimization of a general quadratic function with two special quadratic constraints. Some peculiarities of the problem, mainly with respect to the signs of the eigenvalues of the Hessian of the Lagrangian function at a solution are investigated. The main result is that the Hessian of the Lagrangian has at most one negative eigenvalue if the Lagrangian multipliers are unique. An example is presented to show that the Hessian may have a negative eigenvalue when one constraint is inactive at the solution.
[M.Todorov]

MSC 2000:: *90C20 Quadratic programming
65K05 Mathematical programming (numerical methods)
90-08 Computational methods (optimization)
90C30 Nonlinear programming

Keywords: trust region algorithms; constrained optimization; equality constraints; quadratic function; signs of the eigenvalues; Hessian of the Lagrangian function

Cited in: Zbl 1218.90195 Zbl 0970.90058 Zbl 0837.15022 Zbl 0808.90122 Zbl 0749.90058

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