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Metody s proměnnou metrikou s omezenou pamětí, založené na invariantních maticích
Vlček, Jan ; Lukšan, Ladislav
A new class of limited-memory variable metric methods for unconstrained minimization is described. Approximations of inverses of Hessian matrices are based on matrices which are invariant with respect to a linear transformation. As these matrices are singular, they are adjusted for a computation of direction vectors. The methods have the quadratic termination property, which means that they will find a minimum of a strict quadratic function with an exact choice of a step-length after a finite number of steps. Numerical experiments show the efficiency of this method.
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Metody vnitřních bodů pro zobecněnou minimaxovou optimalizaci
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
A new class of primal interior point methods for generalized minimax optimization is described. These methods use besides a standard logarithmic barrier function also barrier functions bounded from below which have more favourable properties for investigation of global convergence. It deals with descent direction methods, where an approxmation of the Hessian matrix is computed by gradient differences or quasi-Newton updates. Two-level optimization is used. A direction vector is computed by a Choleski decompostition of a sparse matrix. Numerical experiments concerning two basic applications, minimization of a point maximum and a sum of absolute values of smooth functions, are presented.
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