Sökning: "kvadratisk optimering utan bivillkor"

Hittade 2 avhandlingar innehållade orden kvadratisk optimering utan bivillkor.

1. 1. On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization

   Författare :Tove Odland; Anders Forsgren; William W. Hager; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; symmetric system of linear equations; method of conjugate gradients; quasi-Newton method; unconstrained optimization; unconstrained quadratic optimiza- tion; Krylov subspace method; unnormalized Lanczos vectors; minimum-residual method; symmetriska linjära ekvationssystem; konjugerade gradientmetoden; kvasi- Newtonmetoder; optimering utan bivillkor; kvadratisk optimering utan bivillkor; Kry- lovunderrumsmetoder; icke-normaliserade Lanczosvektorer; minimum-residualmetoden; Mathematics; Matematik;

   Sammanfattning : In this thesis we present research on mathematical properties of methods for solv- ing symmetric systems of linear equations that arise in various optimization problem formulations and in methods for solving such problems.In the first and third paper (Paper A and Paper C), we consider the connection be- tween the method of conjugate gradients and quasi-Newton methods on strictly convex quadratic optimization problems or equivalently on a symmetric system of linear equa- tions with a positive definite matrix. LÄS MER

3. 2. Approaches to accelerate methods for solving systems of equations arising in nonlinear optimization

   Författare :David Ek; Anders Forsgren; Jacek Gondzio; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Nonlinear optimization; mathematical programming; interior-point methods; approximate solutions to systems of linear equations; method of conjugate gradients; quasi-Newton methods; modified Newton methods; Ickelinjär optimering; matematisk programmering; inre-punktsmetoder; approximativa lösningar till linjära ekvationssystem; konjugerade gradientmetoden; kvasi-Newtonmetoder; modifierade Newtonmetoder.; Optimization and Systems Theory; Optimeringslära och systemteori;

   Sammanfattning : Methods for solving nonlinear optimization problems typically involve solving systems of equations. This thesis concerns approaches for accelerating some of those methods. In our setting, accelerating involves finding a trade-off between the computational cost of an iteration and the quality of the computed search direction. LÄS MER