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"The new edition of mathematical modeling, the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries.From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, mathematical modeling, fourth edition provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models."

"Perluasan dari Traveling Salesman Problem (TSP) adalah Multiple Traveling Salesman Problem (MTSP), yaitu menentukan kumpulan rute oleh 𝑚 salesman yang berawal dan kembali ke kota asal (depot). Jika terdapat lebih dari satu depot dan salesman yang berawal dan kembali ke depot yang sama, maka permasalahan tersebut dinamakan Fixed Destination Multi-depot Multiple Traveling Salesman Problem (MMTSP). Pada makalah ini, MMTSP akan diselesaikan menggunakan algoritma Ant Colony Optimization (ACO). ACO adalah algoritma optimisasi metaheuristic yang terinspirasi oleh perilaku semut dalam mencari jalur terpendek dari sarang menuju sumber makanan.Dalam penyelesaian MMTSP, akan diamati dengan memerhatikan pemilihan kota yang berbeda sebagai depot dan tiga parameter MMTSP non-random, banyaknya salesman (𝑚), minimum banyaknya kota yang harus dikunjungi salesman (𝐾), dan maksimum banyaknya kota yang dapat dikunjungi salesman (𝐿). Implementasi dilakukan dengan mengambil empat data dari TSPLIB. Hasil implementasi menunjukkan bahwa pemilihan kota yang berbeda sebagai depot dan tiga parameter MMTSP, di mana 𝑚 adalah parameter yang paling esensial, mempengaruhi solusi.

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An extension of Traveling Salesman Problem (TSP) is the Multiple Traveling Salesman Problem (MTSP) in which, determining set of routes by 𝑚 salesmen who all start from and return to a single home city (depot). If there is more than one depot and salesmen start from and return to the same depot, then the problem is called Fixed Destination Multi-depot Multiple Traveling Salesman Problem (MMTSP). In this paper, MMTSP will be solved using the Ant Colony Optimization (ACO) algorithm. ACO is a metaheuristic optimization algorithm which inspired by the behavior of ants in finding the shortest path from the nest to the food source.

In solving the MMTSP, the algorithm is observed with respect to different chosen cities as depots and non-randomly three parameters of MMTSP, the number of salesmen (𝑚), the minimum number of cities a salesman must visit (𝐾), and the maximum number of cities that a salesman can visit (𝐿). The implementation is observed with four dataset from TSPLIB. The results show that both the different chosen cities as depots and the three parameters of MMTSP, in which 𝑚 is the most essential parameter, affect the solution."

"Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. The marriage of mature CFD methodologies with state-of-the-art optimization methods has become the center of activity in computational flow control and optimization.Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, such as choices to be made and difficulties to overcome. He provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems to be aware of when implementing the algorithms.This book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Both those interested in developing new algorithms and those interested in the application of existing algorithms should find useful information in this book."

"This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.The author begins with a general presentation of material pertinent to continuous optimization theory, phrased so as to be readily applicable in developing interior-point method theory. This presentation is written in such a way that even motivated Ph.D. students who have never had a course on continuous optimization can gain sufficient intuition to fully understand the deeper theory that follows. Renegar continues by developing the basic interior-point method theory, with emphasis on motivation and intuition. In the final chapter, he focuses on the relations between interior-point methods and duality theory, including a self-contained introduction to classical duality theory for conic programming; an exploration of symmetric cones; and the development of the general theory of primal-dual algorithms for solving conic programming optimization problems.Rather than attempting to be encyclopedic, A Mathematical View of Interior-Point Methods in Convex Optimization gives the reader a solid understanding of the core concepts and relations, the kind of understanding that stays with a reader long after the book is finished."

"Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized."

"Recent and ongoing improvements in computer technology have increased the need for efficient and reliable design tools; computational methods have opened the door to making sensitivity analysis a tractable design tool for industries that design and manufacture high performance products. These industries are increasingly interested in exploiting the advantages of computer-aided design, numerical analysis, and optimal design methods. This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations."

"In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems."

""The purpose of the book is to give the reader a working knowledge of optimization theory and methods"--"

"Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.The basic idea of the LMI method in control is to approximate a given control problem via an optimization problem with linear objective and so-called LMI constraints. The LMI method leads to an efficient numerical solution and is particularly suited to problems with uncertain data and multiple (possibly conflicting) specifications.Since the early 1990s, with the development of interior-point methods for solving LMI problems, the LMI approach has gained increased interest. One advantage of this technique is its ability to treat large classes of control problems via efficient numerical tools. This approach is widely applicable, not only in control but also in other areas where uncertainty arises. LMI techniques provide a common language for many engineering problems. Notions now popular in control, such as uncertainty and robustness, are being used in other areas through the use of LMIs. This technique is particularly attractive for industrial applications. It is well suited for the development of CAD tools that help engineers solve analysis and synthesis problems."

"Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control."