We develop an algorithm for the linear ordering problem, which has a large number of applications such as triangulation of input-output matrices, minimizing total weighted completion time in one-machine scheduling, and aggregation of individual preferences. The algorithm is based on the Lagrangian relaxation of a binary integer linear programming formulation of the problem. Since the number of ...

The most of nonsmooth optimization methods may be divided in two main groups: subgradient methods and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. In this report we test and compare both different bundle methods and different subgradient methods as well as some methods which may be considered as hybrids of the...

We present a unifying framework for nonsmooth convex minimization bringing together -subgradient algorithms and methods for the convex feasibility problem. This development is a natural step for -subgradient methods in the direction of constrained optimization since the Euclidean projection frequently required in such methods is replaced by an approximate projection, which is often easier to co...

In this paper we develop a subgradient optimization methodology for convex multiparametric nonlinear programs. We define a parametric subgradient, extend some classical optimization results to the multiparametric case, and design a subgradient algorithm that is shown to converge under traditional conditions. We use this algorithm to solve two illustrative example problems and demonstrate its ac...

Abstract In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding common solution of Variational Inequality Problem (VIP) and the fixed point quasi-nonexpansive mapping in 2-uniformly convex uniformly smooth Banach space. The TRSSEM does not require computation projection onto feasible set VIP; instead, it us...

The Traveling Salesman Problem (TSP) is a classical Combinatorial Optimization problem, which has been intensively studied. The Lagrangean relaxation was first applied to the TSP in 1970. The Lagrangean relaxation limit approximates what is known today as HK (Held and Karp) bound, a very good bound (less than 1% from optimal) for a large class of symmetric instances. It became a reference bound...

This paper presents a distributed scheduling methodology for a two-machine flowshop problem. It is assumed that the decision authorities and information are distributed in multiple sub-production systems that must share two machines in order to satisfy their demands. The associated scheduling problems are modeled using 0/1 integer formulations, and the problem is solved using Lagrangian relaxat...

We investigate collaborative optimization in a multi-agent setting, when the agents execute in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, independent of other time instances. Specifically, we study the performance of the consensus-based multi-agent subgradient method, for t...