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We discuss a possibility of the extension of a primal-dual interior-point algorithm suggested recently in 1]. We consider optimization problems deened on the intersection of a symmetric cone and an aane subspace. The question of solvability of a linear system arising in the implementation of the primal-dual algorithm is analyzed. A nondegeneracy theory for… (More)

- Martin Buss, Leonid Faybusovich, John B. Moore
- I. J. Robotics Res.
- 1998

One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp slability and minimum grasping effort. A companion paper shows that the nonlinear friction-force limit constraints on grasping forces are equivalent to the positive definiteness of a certain matrix subject to… (More)

We consider the linear monotone complementarity problem for domains obtained as the intersection of an aane subspace and the Cartesian product of symmetric cones. A primal-dual potential reduction algorithm is described and its complexity estimates are established with the help of the Jordan-algebraic technique .

We introduce a family of compatible Poisson brackets on the space of rational functions with denominator of a fixed degree and use it to derive a multi-Hamiltonian structure for a family of integrable lattice equations that includes both the standard and the relativistic Toda lattices. PACS 02.30, 05.45, 11.30.N

It has recently been shown that the logarithmic barrier method for solving nite-dimensional, linearly constrained quadratic optimization problems can be extended to an in nite-dimensional setting with complexity estimates similar to the nite dimensional case. As a consequence, an e cient computational method for solving the linearly constrained LQ control… (More)

2 Duality, central trajectories and We develop an interior-point technique for soiving quadratic dynamical systems programming problem in a Hilbert space.As an example we consider an application of these results to the linear-quadratic control problem with linear inequality constraints. It is shown that the Newton step in this situation is basically reduced… (More)

- Leonid Faybusovich
- SIAM J. Matrix Analysis Applications
- 1995

- Leonid Faybusovich, Takashi Tsuchiya
- Math. Program.
- 2003

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for… (More)

- Leonid Faybusovich
- SIAM Journal on Optimization
- 2006

We describe a Jordan-algebraic version of results related to convexity of images of quadratic mappings as well as related results on exactness of symmetric relaxations of certain classes of nonconvex optimization problems. The exactness of relaxations is proved based on rank estimates. Our approach provides a unifying viewpoint on a large number of… (More)

- Leonid Faybusovich
- SIAM Journal on Optimization
- 1996