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)
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 .
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 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. 1 It has been known since Moser's work on finite non-periodic Toda… (More)
For the nite Schur (dmKdV) ows, a nonlocal Poisson structure is introduced and shown to be linked via BB acklund-Darboux transformations to linear and quadratic Poisson structures for the Toda lattice. Two diierent Lax representation for the Schur ows are used, one to construct BB acklund-Darboux transformations, the other to solve the Cauchy problem via… (More)
We generalize Nesterov's construction for the reduction of various classes of semi-innnite programming problems to the semideenite programming form. In this way, we are able to consider "cones of squares" of real-valued and matrix-valued functions as rather particular cases of a unifying abstract scheme. We also interpret from this viewpoint some results of… (More)
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)
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 Eu-clidean 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)