On methods for minimizing a function without calculating its derivatives

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Trust-region based methods for unconstrained global optimization

Convexity is an essential characteristic in optimization. In reality, many optimization problems are not unimodal which make their feasible regions to be non-convex. These conditions lead to hard global optimization issues even in low dimension. In this study, two trusted-region based methods are developed to deal with such problems. The developed methods utilize interval technique to find regions where minimizers reside. These identified regions are convex with at least one local minimizer. The developed methods have been proven to satisfy descent property, global convergence and low time complexities. Some benchmark functions with diverse properties have been used in the simulation of the developed methods. The simulation results show that the methods can successfully identify all the global minimizers of the unconstrained non-convex benchmark functions. This study can be extended to solve constrained optimization problems for future work

Application of mathematical programming techniques to power system optimization

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Basis descent methods for convex essentially smooth optimization with applications to quadratic/entropy optimization and resource allocation

Cover title.Includes bibliographical references (p. 33-38).Partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems) DAAL03-86-K-0171 Partially supported by the National Science Foundation. NSF-ECS-8519058by Paul Tseng

The Lagrangean saddle-function as a basis for automated design

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Algorithm for Proportional Matrices in Reals and Integers

Let R be the set of nonnegative matrices whose row and column sums fall between specific limits and whose entries sum to some fixed h > 0. Closely related axiomatic approaches have been developed to ascribe meanings to the statements: the real matrix fe R and the integer matrix a ~ R are "proportional to" a given matrix p ~> 0. These approaches are described, conditions under which proportional solutions exist are characterized, and algorithms are given for finding proportional solutions in each case.algorithm ; proportional matrices

An allocation based modeling and solution framework for location problems with dense demand /

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm

Numerical Techniques for Stochastic Optimization

This is a comprehensive and timely overview of the numerical techniques that have been developed to solve stochastic programming problems. After a brief introduction to the field, where accent is laid on modeling questions, the next few chapters lay out the challenges that must be met in this area. They also provide the background for the description of the computer implementations given in the third part of the book. Selected applications are described next. Some of these have directly motivated the development of the methods described in the earlier chapters. They include problems that come from facilities location, exploration investments, control of ecological systems, energy distribution and generation. Test problems are collected in the last chapter. This is the first book devoted to this subject. It comprehensively covers all major advances in the field (both Western and Soviet). It is only because of the recent developments in computer technology, that we have now reached a point where our computing power matches the inherent size requirements faced in this area. The book demonstrates that a large class of stochastic programming problems are now in the range of our numerical capacities

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications