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"separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions. Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming. Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful self-contained appendices on vectors and matrices, topological properties of n-dimensional real space, continuity and minimization, and differentiable functions."

"A reprint of the original volume, which won the Lanchester Prize awarded by the Operations Research Society of America for the best work of 1968. Although out of print for nearly 15 years, it remains one of the most referenced volumes in the field of mathematical programming. Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them."

"This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization."

"[ABSTRAKPermasalahan newsboy merupakan permasalahan memaksimumkan keuntungan pada produk yang mempunyai batas waktu penjualan dan jumlah permintaan yang belum pasti. Skripsi ini membahas permasalahan newsboy multiproduk dengan kapasitas penyimpanan gudang terbatas. Untuk mengatasi kekurangan produk akibat kapasitas penyimpanan gudang yang terbatas, penjual membeli produk di luar agen utama yang disebut agen outsourcing. Permasalahan newsboy ini dimodelkan ke dalam masalah nonlinear programming. Selanjutnya dijelaskan karakteristik solusi optimal dari permasalahan ini sehingga didapatkan solusi optimalnya.

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ABSTRACTNewsboy problems is the problem of maximizing profits on products that have a time limit of sales and uncertain demand. This skripsi discuss multi-product newsboy problem with limited storage capacity. To deal with possible shortage of the product due to the limited storage capacity, the seller buy products outside the main agent called outsourcer. This newsboy problems can be modeled into a nonlinear programming problem. Next will be explained the properties of the optimal solution of this problem to obtain the optimal solution.;Newsboy problems is the problem of maximizing profits on products that have a time limit of sales and uncertain demand. This skripsi discuss multi-product newsboy problem with limited storage capacity. To deal with possible shortage of the product due to the limited storage capacity, the seller buy products outside the main agent called outsourcer. This newsboy problems can be modeled into a nonlinear programming problem. Next will be explained the properties of the optimal solution of this problem to obtain the optimal solution., Newsboy problems is the problem of maximizing profits on products that have a time limit of sales and uncertain demand. This skripsi discuss multi-product newsboy problem with limited storage capacity. To deal with possible shortage of the product due to the limited storage capacity, the seller buy products outside the main agent called outsourcer. This newsboy problems can be modeled into a nonlinear programming problem. Next will be explained the properties of the optimal solution of this problem to obtain the optimal solution.]"

"Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization."

"Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences.The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely. By providing the necessary proofs and presenting the material in a conversational style, Franklin made Methods of Mathematical Economics extremely popular among students. The addition of a list of errata, new to this edition, should add to the book's popularity as well as its usefulness both in the classroom and for individual study.The book has three chapters: "Linear Programming," "Nonlinear Programming," and "Fixed-Point Theorems." The first and third chapters include the economic equilibrium theorems of von Neumann and of J. F. Nash, while the second chapter includes Kuhn-Tucker theory and Wolfe's simplex algorithm for quadratic programming. The book concludes with easy, elementary proofs of the famous theorems of Brouwer, of Kakutani, and of Schauder. These fundamental results are usually proved only in advanced texts in topology, economic theory, and nonlinear analysis."

"This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides flexibility to accommodate the varying needs of instructors, students, and practitioners with different levels of sophistication in these topics. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines."

"Pertumbuhan industri otomotif yang semakin meningkat di Indonesia belum diimbangi dengan jumlah pemasok bahan baku lokal dan membuat industri otomotif bergantung pada aktivitas impor. Seiring dengan banyaknya kebutuhan aktivitas impor ini, maka dibutuhkan pula aktivitas logistik yang lebih besar. Namun dengan biaya logistik yang tinggi, membuat perusahaan harus meningkatkan efisiensi untuk dapat terus bersaing dalam industri nasional. Oleh karena itu, perlu adanya perencanaan aktivitas inbound logistik yang mengatur pergerakan material dari pemasok hingga sampai ke pabrik. Pada penelitian ini, dikembangkan sebuah model optimasi menggunakan pendekatan pemrograman non linier integer campuran yang diselesaikan dengan algoritma branch and bound. Hasil dari penelitian ini, yaitu didapatkan total biaya inbound logistik yang optimal mencakup biaya material, biaya transportasi, dan biaya pelabuhan. Model ini juga dapat digunakan sebagai alat bantu perusahaan dalam pengambilan keputusan mengenai tipe kontainer dan jumlah kontainer yang digunakan beserta total muatan yang optimal dalam setiap kontainer, sehingga didapatkan nilai utilasi kontainer yang tinggi.

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The increasing growth of automotive industry in Indonesia has not been matched by the number of local suppliers and makes the automotive industry too dependent on imported raw materials. Along with the needs of import activities, it is also required a greater logistics activities. However, with high logistics costs, the manufacturer must increase efficiency to be able compete in the global market. This can be accomplished by planning inbound logistics activities that control the movement of materials from suppliers to the manufacture.

In this research, an optimization methodology, based on Mixed Integer Nonlinear Programming MINLP approach is developed and solved with branch and bound algorithm.

The result of this research, which obtained the total cost of optimal inbound logistics include material cost, transportation cost, and administration cost. This model can also be used as a tool for the company in making decisions about the type and the number of container also with the total of the optimal material load in each container, therefore the optimal container space utilization value can be obtained."