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


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