Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutti...

Multicommodity flows belong to the class of primal block-angular problems. An efficient interior-point method has already been developed for linear and quadratic network optimization problems. It solved normal equations, using sparse Cholesky factorizations for diagonal blocks, and a preconditioned conjugate gradient for linking constraints. In this work we extend this procedure, showing that t...

Balinski and Tucker introduced in 1969 a special form of optimal tableaus for LP, which can be used to construct primal and dual optimal solutions such that the complementary slackness relation holds strictly. In this paper, first we note that using a polynomial time algorithm for LP Balinski and Tucker’s tableaus are obtainable in polynomial time. Furthermore, we show that, given a pair of pri...

In this paper we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions the error bounds for the primal and dual sequences converge to zer...

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the ...

An adaptive choice for primal spaces, based on parallel sums, is developed for BDDC deluxe methods and elliptic problems in three dimensions. The primal space, which form the global, coarse part of the domain decomposition algorithm, and which is always required for any competitive algorithm, is defined in terms of generalized eigenvalue problems related to subdomain edges and faces; selected e...

Constrained Markov Decision Process (CMDP) is a natural framework for reinforcement learning tasks with safety constraints, where agents learn a policy that maximizes the long-term reward while satisfying the constraints on the long-term cost. A canonical approach for solving CMDPs is the primal-dual method which updates parameters in primal and dual spaces in turn. Existing methods for CMDPs o...

In this thesis, we study primal solutions for general optimization problems. In particular, we employ the subgradient method to solve the Lagrangian dual of a convex constrained problem, and use a primal-averaging scheme to obtain near-optimal and near-feasible primal solutions. We numerically evaluate the performance of the scheme in the framework of Network Utility Maximization (NUM), which h...

the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

statement of the problem: implant-retained overdenture can improve the stability of dentures and prevent bone loss. overdenture-wearing patients need special hygiene care. purpose: the aim of this study was to evaluate the effects of various denture cleansers on the retention of dio orange o-rings. method and materials : in this experimental study, 40 dio orange o-rings were divided into 4 grou...