TY - RPRT TI - Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations AU - Vlček, Jan AB - Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods. UR - http://hdl.handle.net/11104/0310865 UR - http://www.nusl.cz/ntk/nusl-432144 A2 - Lukšan, Ladislav LA - eng KW - variable metric methods KW - unconstrained minimization KW - variationally derived methods KW - global convergence KW - numerical results KW - limited-memory methods UR - http://invenio.nusl.cz/record/432144/files/0532367-V-1280.pdf PY - 2020 PB - Ústav informatiky, Pod vodárenskou věží 2, 182 07 Praha 8, http://www.cs.cas.cz/ ER -