In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...

L BFGS B is a limited memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables It is intended for problems in which information on the Hessian matrix is di cult to obtain or for large dense problems L BFGS B can also be used for unconstrained problems and in this case performs similarly to its predecessor algorithm L BFGS Harwell routine VA Th...

We present a newmatrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of ...

In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...

In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...

In this paper, we investigate a formula to solve systems of the form (Bk + D)x = y, where Bk comes from a limited-memory BFGS quasi-Newton method and D is a diagonal matrix with diagonal entries di,i ≥ σ for some σ > 0. These types of systems arise naturally in large-scale optimization. We show that provided a simple condition holds on B0 and σ, the system (Bk + D)x = y can be solved via a recu...

On the platform of general chemical process simulation software (it was named Optimization Engineer, OPEN), a optimization algorithm for is developed using C + code. The based on sequential quadratic programming (SQP). We adopt activity set and rotation axis to generate solve sub-problem. active method can simplify number constraints speed up calculation. At same time, we used limited memory BF...

Energy minimization plays an important role in structure determination and analysis of proteins, peptides and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently Morales and Nocedal have developed enriched methods for large scale unconstrained optimization that interlace iterations of the limited memory BFGS method (L-BFGS) and the Hessian...

The Broyden family of quasi-Newton methods for unconstrained optimization will be considered. It is well-known that if a member of this family is defined su ciently close to that of the robust BFGS method, then useful theoretical and numerical properties are obtained. These properties will be extended to all members of the above family provided that the current points are su ciently close to th...