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.

Sequential Quadratic Programming Methods

Abstract: In his 1963 PhD thesis, Wilson proposed the first sequential quadratic programming (SQP) method for the solution of constrained nonlinear optimization problems. In the intervening 48 years, SQP methods have evolved into a powerful and effective class of methods for a wide range of optimization problems. We review some of the most prominent developments in SQP methods since 1963 and discuss the relationship of SQP methods to other popular methods, including augmented Lagrangian methods and interior methods. Given the scope and utility of nonlinear optimization, it is not surprising that SQP methods are still a subject of active research. Recent developments in methods for mixed integer nonlinear programming (MINLP) and the minimization of functions subject to differential equation constraints has led to a heightened interest in methods that may be “warm started” from a good approximate solution. We discuss the role of SQP methods in these contexts

Scenario-Based Multiobjective Volt/Var Control in Distribution Networks Including Renewable Energy Sources

Abstract: This paper proposes a stochastic multiobjective framework for daily volt/var control (VVC), including hydroturbine, fuel cell, wind turbine, and photovoltaic powerplants The multiple objectives of the VVC problem to be minimized are the electrical energy losses, voltage deviations, total electrical energy costs, and total emissions of renewable energy sources and grid For this purpose, the uncertainty related to hourly load, wind power, and solar irradiance forecasts are modeled in a scenario-based stochastic framework A roulette wheel mechanism based on the probability distribution functions of these random variables is considered to generate the scenarios Consequently, the stochastic multiobjective VVC (SMVVC) problem is converted to a series of equivalent deterministic scenarios Furthermore, an Evolutionary Algorithm using the Modified Teaching-Learning-Algorithm (MTLA) is proposed to solve the SMVVC in the form of a mixed-integer nonlinear programming problem In the proposed algorithm, a new mutation method is taken into account in order to enhance the global searching ability and mitigate the premature convergence to local minima Finally, two distribution test feeders are considered as case studies to demonstrate the effectiveness of the proposed SMVVC

On the Convergence of a Sequential Quadratic Programming Method with an Augmented Lagrangian Line Search Functions.

Abstract: Sequential quadratic programming methods as developed by Wilson, Han, and Powell have gained considerable attention in the last few years mainly because of their outstanding numerical performance. Although the theoretical convergence aspects of this method and its various modifications have been investigated in the literature, there still remain some open questions which will be treated in this paper. The convergence theory to be presented, takes into account the additional variable introduced in the quadratic programming subproblem to avoid inconsistency, the one-dimensional minimization procedure, and, in particular, an “ active set” strategy to avoid the recalculation of unnecessary gradients. This paper also contains a detailed mathematical description of a nonlinear programming algorithm which has been implemented by the author. the usage of the code and detailed numerical test results are presented in [5].

Efficient monte carlo technique for locating critical slip surface

Abstract: The search for the critical slip surface in slope-stability analysis is performed by means of a minimization of the safety factor. The procedures most widely used are deterministic methods of nonlinear programming, and random search methods have been neglected, since they are considered to be generally less efficient. In this paper, an efficient Monte-Carlo method for locating the critical slip surface is presented. The procedure is articulated in a sequence of stages, where each new slip surface is randomly generated by an appropriate technique. From a comparative analysis, the proposed method provides solutions of the same quality as the best nonlinear programming methods. However, the structure of the presented method is very simple, and it can be more easily programmed, integrated, and modified for particular exigencies.