Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Optimal Operation of Distribution Feeders in Smart Grids

Abstract: This paper presents a generic and comprehensive distribution optimal power flow (DOPF) model that can be used by local distribution companies (LDCs) to integrate their distribution system feeders into a Smart Grid. The proposed three-phase DOPF framework incorporates detailed modeling of distribution system components and considers various operating objectives. Phase specific and voltage dependent modeling of customer loads in the three-phase DOPF model allows LDC operators to determine realistic operating strategies that can improve the overall feeder efficiency. The proposed distribution system operation objective is based on the minimization of the energy drawn from the substation while seeking to minimize the number of switching operations of load tap changers and capacitors. A novel method for solving the three-phase DOPF model by transforming the mixed-integer nonlinear programming problem to a nonlinear programming problem is proposed which reduces the computational burden and facilitates its practical implementation and application. Two practical case studies, including a real distribution feeder test case, are presented to demonstrate the features of the proposed methodology. The results illustrate the benefits of the proposed DOPF in terms of reducing energy losses while limiting the number of switching operations.

Stability of queueing networks and scheduling policies

Abstract: We develop a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steady-state probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems. >

Solving the Trust-Region Subproblem using the Lanczos Method

Abstract: The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, the most widely used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust-region boundary. In this paper, we investigate ways of continuing the process once the boundary has been encountered. The key is to observe that the trust-region problem within the currently generated Krylov subspace has a very special structure which enables it to be solved very efficiently. We compare the new strategy with existing methods. The resulting software package is available as HSL_VF05 within the Harwell Subroutine Library.

A simulated annealing algorithm for unit commitment

Abstract: This paper presents a simulated annealing algorithm (SAA) to solve the unit commitment problem (UCP). New rules for randomly generating feasible solutions are introduced. The problem has two subproblems: a combinatorial optimization problem; and a nonlinear programming problem. The former is solved using the SAA while the latter problem is solved via a quadratic programming routine. Numerical results showed an improvement in the solutions costs compared to previously obtained results.