On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

Dendronized polymers via Diels–Alder “click” reaction

A modular approach toward the synthesis of polymers containing dendron groups as side chains is developed using the Diels–Alder “click” reaction. For this purpose, a styrene‐based polymer appended with anthracene groups as reactive side chains was synthesized. First through third‐generation polyester dendrons containing furan‐protected maleimide groups at their focal point were synthesized. Facile, reagent‐free, thermal Diels–Alder cycloaddition between the anthracene‐containing polymer and latent‐reactive dendrons leads to quantitative functionalization of the polymer chains to afford dendronized polymers. The efficiency of this functionalization step was monitored using ¹H and ¹³C NMR spectroscopy and FTIR and UV–vis spectrometry. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 410–416, 2010     

A coradiant based scalarization to characterize approximate solutions of vector optimization problems with variable ordering structures

This paper investigates some properties of approximate efficiency in variable ordering structures where the variable ordering structure is given by a special set valued map. We characterize $\epsilon$-minimal and $\epsilon$- nondominated elements as approximate solutions of a multiobjective optimization problem with a variable ordering structure and give necessary and sufficient conditions for these solutions, via scalarization.     

Optimality conditions in nonconvex optimization via weak subdifferentials

In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented.     

A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems.     

Properly optimal elements in vector optimization with variable ordering structures

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.     

A generalization of a theorem of Arrow,Barankin and Blackwell to a nonconvex case

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.     

Synthesis of cationic N‐[3‐(dimethylamino)propyl]methacrylamide brushes on silicon wafer via surface‐initiated RAFT polymerization

Surface‐initiated reversible addition‐fragmentation chain transfer (SI‐RAFT) polymerization of N‐[3‐(dimethylamino)propyl]methacrylamide (DMAPMA) on the silicon wafer was conducted in attempt to create controllable cationic polymer films. The RAFT agent‐immobilized substrate was prepared by the silanization of hydroxyl groups on silicon wafer with 3‐aminopropylthriethoxysilane (APTS) and by the amide reaction of amine groups of APTS with ester groups of 4‐cyano‐4‐((thiobenzoyl) sulfanyl) pentanoic succinimide ester (CPSE); followed by the RAFT polymerization of DMAPMA using a “free” RAFT agent, that is, 4‐cyanopentanoic acid dithiobenzoate (CPAD) and an initiator, that is, 4,4′‐azobis‐4‐cyanopentanoic acid (CPA). The formation of homogeneous tethered poly(N‐[3‐(dimethylamino)propyl]methacrylamide) [poly(DMAPMA)] brushes, whose thickness can be tuned by reaction time varying, is evidenced by using the combination of grazing angle attenuated total reflectance‐Fourier transform infrared spectroscopy, X‐ray photoelectron spectroscopy, atomic force microscopy, and water contact‐angle measurements. The calculation of grafting parameters from the number‐average molecular weight, M _n (g/mol) and ellipsometric thickness, h (nm) values indicated the synthesis of densely grafted poly(DMAPMA) films and allowed us to predict a polymerization time for forming a “brush‐like” conformation for the chains. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011