Log-barrier method for two-stage quadratic stochastic programming
The author consider the following two-stage quadratic stochastic programs \[ \min c^Tx+ \textstyle{{1\over 2}} x^T Px+ \rho(x)\quad\text{s.t. }Ax= b,\quad x\geq 0, \] where \(P\) is symmetric positive definite and \(\rho(x)\) is the recourse function defined by \(\rho(x)= E[\rho(x,\widetilde\zeta)]\), where, for each realization \(\zeta\in \Xi\) \[ \rho(x,\zeta):= \min q(\zeta)^T y(\zeta)+\textstyle{{1\over 2}}y(\zeta)^T D(\zeta) y(\zeta)\,\text{ s.t. }T(\zeta)x+ W(\zeta) y(\zeta)= h(\zeta),\;y(\zeta)\geq 0. \] For the solution, a log-barrier algorithm is presented. Properties of the given algorithm are discussed and the convergence and complexity of the given algorithm is analysed.
Two-stage quadratic stochastic programming
scientific article; zbMATH DE number 2165259