Study of non-linear optimization techniques

Nonlinear optimization techniques in dynamic programming and solution of ordinary nonlinear differential equations by Runge-Kutta metho

Particulars of Non-Linear Optimization

We are providing a concise introduction to some methods for solving non-linear optimization problems. In mathematics,non-linear programming (NLP) is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are non-linear. It is the sub-field of mathematical optimization that deals with problems that are not linear. This dissertation conducts its study on the theory that are necessary for understanding and implementing the optimization and an investigation of the algorithms such as Wolfe's Algorithm, Dinkelbach's Algorithm and etc. are available for solving a special class of the non-linear programming problem, quadratic programming problem which is included in the course of study. Optimization problems arise continuously in a wide range of fields such as Power System Control and thus create the need for effective methods of solving them. We discuss the fundamental theory necessary for the understanding of optimization problems, with particular programming problems and the algorithms that solve such problems

Some aspects of non-linear optimization

We provide a concise introduction to some methods for solving nonlinear optimization problems. This dissertation includes a literature study of the formal theory necessary for understanding optimization and an investigation of the algorithms available for solving a special class of the non-linear programming problem, namely the quadratic programming problem. It was not the intention of this dissertation to discuss all possible algorithms for solving the quadratic programming problem, therefore certain algorithms for convex and non-convex quadratic programming problems . Some of the algorithms were selected arbitrarily, because limited information was available comparing the eciency of the various algorithms

SOCIAL WELFARE AND ENVIRONMENTAL DEGRADATION IN AGRICULTURE: THE CASE OF ECUADOR

A non-linear optimization model which maximizes total Ecuadorian social welfare, defined as the sum of consumers' and producers' surpluses for the four major crops (corn, bananas, rice and African palm) is developed to evaluate the tradeoff between welfare and environmental degradation in Ecuador. It was found that a total welfare loss of US$122 million (a 11 percent reduction - from US$ 1.112 billion to US$ 989.66 million) would be expected from a 30 percent reduction in the total pesticide load on the environment in the production of the four major crops. The distributional impacts of the welfare loss were found, however, to be significantly skewed toward the loss of consumers' surplus. Specifically, a 30 percent reduction of total pesticide load on the environment would result in a reduction of 3.86 percent of producers' total surplus while consumers would be expected to loose 19.46 percent of their total surplus.welfare tradeoff, environmental impacts, non-linear optimization, Environmental Economics and Policy,

Non-Linear Optimization Applied to Angle-of-Arrival Satellite-Based Geolocation

Geolocation is a common application for satellite systems. This involves estimating an object\u27s location (herein called the subject) based on noisy satellite data. Many geolocation methods exist; however, none are tailored specifically for the unique problems faced by satellite systems. Some satellites are so far from the subject being localized that by the time the satellite receives a signal from the subject it might have moved appreciably. Furthermore, some satellites or terrestrial sensors may be much closer to the subject than others. Therefore, sensors may need to be weighted based upon their distance to the subject being localized. In addition, even if a subject can be localized, the confidence in this localization may be unknown. Non-linear optimization is proposed, implemented, and analyzed as a means of geolocating objects and providing confidence estimates from passive satellite line-of-sight data. Non-linear optimization requires an initial estimate. This estimate is provided by a triangulation method. The non-linear optimization then improves upon this estimate iteratively by finding estimates that are more likely to have produced the observed line-of-sight measurements. The covariance matrix of the geolocation parameters being estimated is naturally produced by the optimization which provides quantified confidence in the geolocation estimate. Simulations are developed to provide a means of evaluating the performance of the non-linear optimization algorithm. It was found that non-linear optimization can reduce the average error in geolocation estimates, provide improved estimation confidence, and accurately estimate its geolocation confidence for some subjects. The results from the theoretical development of the non-linear optimization algorithm and its simulated performance is quantified and discussed