In a recent paper [8], Chan and Sun reported for semidefinite programming (SDP) that the primal/dual constraint nondegeneracy is equivalent to the dual/primal strong second order sufficient condition (SSOSC). This result is responsible for a number of important results in stability analysis of SDP. In this paper, we study duality of this type in nonlinear semidefinite programming (NSDP). We int...

Our goal is to establish an efficient decomposition of an ideal A of a commutative ring R as an intersection of primal ideals. We prove the existence of a canonical primal decomposition: A = ⋂ P∈XA A(P ), where the A(P ) are isolated components of A that are primal ideals having distinct and incomparable adjoint primes P . For this purpose we define the set Ass(A) of associated primes of the id...

In this paper, we present a simpler proof of the result of Tsuchiya and Muramatsu on the convergence of the primal affine scaling method. We show that the primal sequence generated by the method converges to the interior of the optimum face and the dual sequence to the analytic center of the optimal dual face, when the step size implemented in the procedure is bounded by 2/3. We also prove the ...

In this paper, a primal-dual algorithm for TV-type image restoration is analyzed and tested. Analytically it turns out that employing a global L-regularization, with s > 1, in the dual problem results in a local smoothing of the TV-regularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the `r-norm, with r−1 + s−1 = 1, and a smo...

The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties — 1) each choice of weights uniquely determines a pair of primal-dual weighted centers, and ...

Abstract. In this paper, a FETI-DP formulation for three dimensional elasticity on non-matching grids over geometrically non-conforming subdomain partitions is considered. To resolve the nonconformity of the finite elements, a mortar matching condition is imposed on the subdomain interfaces (faces). A FETI-DP algorithm is then built by enforcing the mortar matching condition in dual and primal ...

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method could be established in terms of 1) the distance from the current iterate to...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗( ) linear complementarity problems (LCPs). We generalize Bai et al.’s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985–1008] primal-dual interior point algorithm for linear optimization (LO) problem to P∗( ) LCPs. New search ...

Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? ...

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel and combines the dual solutions to obtain a new d...