Production and Demand Management

This Chapter ranges through a wide variety of production and demand management problems related to energy commodities systems. The Oil and Gas production enhancement is discussed via oil wells optimal placement as well as water and gas optimal injection, namely waterflooding and gas lift. Further is analyzed the optimal schedule and design of...

A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre et al. (EURO J Comput Optim 1–31, 2015) constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal...

Bound-constrained polynomial optimization using only elementary calculations

We provide a monotone nonincreasing sequence of upper bounds f H k (k≥1) fkH(k≥1) converging to the global minimum of a polynomial <i>f</i> on simple sets like the unit hypercube in ℝ^<i>n</i>. The novelty with respect to the converging sequence of upper bounds in Lasserre [Lasserre JB (2010) A new look at nonnegativity on closed...

On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions

We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also give the tight worst-case...

Interior Point Methods for Semidefinite Programming