1. Decision making and operations research. (a) The need for optimization. (b) Typical models of industry and finance. 2. Advanced linear programming (LP) (a) Need for linear models. (b) General form of LP problems. (c) The sparse simplex method; primal and dual algorithms; computational implications. (d) Economic interpretation of the optimality conditions: Sensitivity analysis. (e) Interior p...

Although inverse linear programming (LP) has received increasing attention as a technique to identify an LP that can reproduce observed decisions are originally from complex system, the performance of objective function inferred by existing methods is often highly sensitive noise, errors, and uncertainty in underlying decision data. Inspired robust regression techniques mitigate impact noisy da...

Abstract— Linear programming (LP) is one of the most important techniques used in modeling and solving practical optimisation problems that arise in industry, commerce and management. It is well known that, for largest LP problems, only a relatively small percentage of constraints are binding at the optimal solution. In fact, large LP problems almost contain a significant number of redundant co...

We consider the integer program P→max{c′x|Ax = y;x ∈ N}. Using the generating function of an associated counting problem, and a generalized residue formula of Brion and Vergne, we explicitly relate P with its continuous linear programming (LP) analogue and provide a characterization of its optimal value. In particular, dual variables λ ∈ R have discrete analogues z ∈ C, related in a simple mann...

Linear Programming Problems are mathematical models used to represent real life situations in the form of linear objective function and constraints various methods are available to solve linear programming problems. When formulating an LP model, systems analysts and researchers often include all possible constraints although some of them may not be binding at the optimal solution. The presence ...

This paper introduces a linear programming (LP) technique that performs ratedistortion based optimization for constrained video coding. Given the assumption of piecewise linear and convex rate-distortion functions, LP is used to generate optimal solutions for the minmax problem under VBR buffer constraints. The LP solution for this problem avoids an explicit search for the minimum distortion va...

Given a linear code and observations from a noisy channel, the decoding problem is to determine the most likely (ML) codeword. We describe a method for approximate ML decoding of an arbitrary binary linear code, based on a linear programming (LP) relaxation that is defined by a factor graph or parity check representation of the code. The resulting LP decoder, which generalizes our previous work...

The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau’s corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project closure. The orig...

We present methods for constructing approximation algorithms to NP-hard optimization problems using linear programming (LP). We typically obtain an LP relaxation of the problem by formulating it as an integer linear program and dropping the integrality constraints. We then solve the LP relaxation exactly, and apply various rounding strategies (including randomized rounding and iterative roundin...