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A modified projection and contraction method for a class of linear complementarity problems. (English) Zbl 0854.65047

For the generalized linear complementarity problems \[ u_i \geq 0,\quad (Mu + q)_i \geq 0,\quad u_i(Mu + q)_i = 0,\quad \text{for } i \in I,\quad (Mu + q)_i = 0,\quad \text{for } i \in L \setminus I, \] where \(L = \{1,\dots,\ell\}\), \(I \subseteq L\), \(M\) is an \(\ell \times \ell\) positive semi-definite matrix and \(q \in \mathbb{R}^\ell\), the author presents a globally convergent projection and contraction method which is a modification of his earlier method [Appl. Math. Optimization 25, No. 3, 247-262 (1992; Zbl 0767.90086)]. He describes the new algorithm and its relation to the original one. The convergence properties of the new algorithm and some numerical results are given.

MSC:

65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Citations:

Zbl 0767.90086
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