## An example of irregular convergence in some constrained optimization methods that use the projected Hessian.(English)Zbl 0576.90079

Consider the problem: minimize $$\{f(x)|\;x\in R_ n\}$$ subject to $$c(x)=0$$ where f is a real-valued function on $$R^ n$$ and c maps $$R^ n$$ to $$R^ m$$, and f and c are twice differentiable. One method for solving such problems, the method of successive quadratic programming, has the form $_{d\in R_ n}\nabla f(x_ k)^ Td+d^ TB_ kd\text{ subject to }\nabla c(x_ k)^ Td=-c(x_ k)$ where $$X_{k+1}=X_ k+d_ k$$. Rates of convergence of algorithms using related methods are discussed. In particular an example is given showing that such methods are not one-step superlinearly convergent.
Reviewer: M.A.Hanson

### MSC:

 90C30 Nonlinear programming 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods
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### References:

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