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? ...

In the following appendices, we provide detailed proofs of theorems stated in the main paper. In Section A we first prove a basic inequality which is useful throughout the rest of the convergence analysis. Section B contains general analysis of the batch primal-dual algorithm that are common for proving both Theorem 1 and Theorem 3. Sections C, D, E and F give proofs for Theorem 1, Theorem 3, T...

Objective(S): In this work, paclitaxel (PX), a promising anticancer drug, was loaded in the basil seed mucilage (BSM) aerogels by implementation of supercritical carbon dioxide (SC-CO2) technology. Then, the effects of operating conditions were studied on the PX mean particle size (MPS), particle size distribution (PSD) and drug loading efficiency (DLE). <stron...

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

A new initialization or ‘Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path — our initial method (Algo...

We consider a Primal-Dual Augmented Lagrangian (PDAL) method for optimization problems with equality constraints. Each step of the PDAL requires solving the Primal-Dual linear system of equations. We show that under the standard second-order optimality condition the PDAL method generates a sequence, which locally converges to the primal-dual solution with quadratic rate.