Khachiyan, and recently Karmarkar, gave polynomial algorithms to solve the linear programming problem. These algorithms have a small theoretical drawback; namely, the number of arithmetic steps ...

Line-Search Methods In each iteration k, the (dual) quasi-Newton, hybrid quasi-Newton, conjugate gradient, and Newton-Raphson minimization techniques use iterative line-search algorithms that try to ...

Formulate linear and integer programming problems for solving commonly encountered optimization problems. Understand how approximation algorithms compute solutions that are guaranteed to be within ...

We give a branch-and-cut algorithm for solving linear programs (LPs) with continuous separable piecewise-linear cost functions (PLFs). Models for PLFs use continuous variables in special-ordered sets ...