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"Mathematical Reviews said of this book that it was "destined to become a classical reference." This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume."

"Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail."

"This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness."

"The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature."

"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."

"Dalam pembangunan kapal baja menjadi item paling banyak dibutuhkan sebagai material kapal. Harga baja cenderung meningkat dari waktu ke waktu seiring dengan krisis global. Hal ini membuat biaya produksi kapal secara keseluruhan meningkat. Hal yang dapat dilakukan untuk menurunkan biaya produksi adalah dengan menurunkan biaya material. Salah satu cara untuk menurunkan biaya material adalah dengan melakukan optimasi pemilihan material. Pada penelitian ini optimasi dilakukan menggunakan Upgrade & Downgrade Method.Ada 3 step yang berjalan pada metode ini. Metode ini bekerja dengan mengganti material yang ketebalannya telah melebihi parameter yang telah ditentukan. Parameter pergantian material ditentukan berdasarkan rangking material. Material rangking 3 akan digantikan material rangking 2 dan seterusnya. Pada step 1 sebagai step awal akan menggunakan material dengan rangking paling rendah sebagai initial design. Hasil dari step 1 akan mengganti material yang memiliki ketebalan melebihi parameter dengan material yang rangkingnya lebih tinggi. Rangking material dihasilkan dari perbandingan antara yield strength dengan harga material. Material yang digunakan dalam penelitian ini adalah mild steel,AH 32 dan AH 36.Untuk menguji efektivitas metode ini, dibuatkan 6 kasus dengan perbedaan harga material setiap kasusnya sehingga menghasilkan rangking material yang bervariasi juga. Hasil dari penelitian ini akan menampilkan perbandingan harga material pada setiap kasusnya. Harga paling rendah yang dihasilkan dari masing-masing step adalah hasil paling optimal dan akan dijadikan final design. Hasil penelitian disajikan dalam bentuk grafik perbandingan harga dan massa. Dari hasil penelitian biaya pada kasus 1 turun sebesar 29.5 % menjadi 8.542.723 rupiah, pada kasus 2 turun sebesar 47.7% menjadi 6.336.328 rupiah, pada kasus 3 turun sebesar 48.1% menjadi 7.070.354 rupiah, pada kasus 4 turun sebesar 49.1% menjadi 7.703.958 rupiah, pada kasus 5 turun sebesar 26.3% menjadi 7.820.365 rupiah dan pada kasus 6 turun sebesar 26.1% menjadi 10.083.541 rupiah.

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In the construction of ships, steel is the most needed item as ship material. Steel prices tend to increase from time to time in line with the global crisis. This makes the overall production cost of ships increase. One thing that can be done to reduce production costs is to reduce material costs. One way to reduce material costs is to optimize material selection. In this research, optimization is carried out using the Upgrade & Downgrade Method. There are 3 steps that run in this method. This method works by replacing the material whose thickness has exceeded the specified parameters. Material replacement parameters are determined based on the material ranking. The 3rd rank material will be replaced by the 2nd rank material and so on. In the first step as an initial step, we will use the material with the lowest rank as the initial design. The results of step 1 will replace the material that has a thickness exceeding the parameter with a material with a higher ranking. Material ranking is generated from the comparison between yield strength and material price. The materials used in this research are mild steel, AH 32 and AH 36. To test the effectiveness of this method, 6 cases were made with differences in material prices in each case in order to produce a varied material ranking as well. The results of this study will show a comparison of material prices in each case. The lowest price generated from each step is the most optimal result and will be used as the final design. The results of the study are presented in a price and mass comparison chart. From the results of the study, the cost in case 1 decreased by 29.5% to 8,542,723 rupiah, in case 2 it decreased by 47.7% to 6,336,328 rupiah, in case 3 it decreased by 48.1% to 7,070,354 rupiah, in case 4 it decreased by 49.1% to 7,703,958 rupiah, in case 5 it decreased by 26.3% to 7,820,365 rupiah and in case 6 it decreased by 26.1% to 10,083,541 rupiah."

"Kegiatan produksi minyak dan gas di lepas pantai tidak dapat dilaksanakan tanpa peran penting dari workover rig barge lepas pantai (Offshore workover rig barge) sebagai alat utama yang digunakan dalam kegiatan operasi intervensi sumur minyak dan gas bumi. Biaya pemakaian peralatan ini menjadi salah satu komponen biaya terbesar dalam setiap kegiatan intervensi sumur tersebut yang bertujuan menjaga laju produksi minyak dan gas perusahaan. Setiap usaha untuk meminimalisasi biaya pemakaian operasi workover rig barge akan memberikan dampak yang signifikan terhadap biaya yang digunakan untuk setiap pekerjaan intervensi sumur. Dalam penelitian ini dilakukan proses optimalisasi terhadap offshore workover rig barge perusahaan CNOOC SES Ltd. Metode yang digunakan adalah mixed integer programming dengan terlebih dahulu memformulasikan model matematis dari operasi workover rig barge. Nilai variabel-variabel keputusan dari model matematis a diperoleh dengan bantuan perangkat lunak optimalisasi Lingo 17.0. Proses optimalisasi menghasilkan pengurangan biaya rata-rata pekerjaan intervensi sumur sebesar 3.59% atau setara dengan US$ 8,518.

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The production activity of offshore oil and gas cannot be sustained without the vital role of offshore workover rig barge as a main tool that is used in oil and gas well intervention operation activity. Rental cost of this equipment is considered as one of the biggest cost components in every well intervention activity which has an objective to maintain company’s oil and gas production rate. Every effort to minimize the rental cost of workover rig barge operation will give significant effect on the cost that is used in every well intervention activity. The objective of this research is to optimize offshore workover rig barge operation in CNOOC SES Ltd. A mathematical model will be formulated prior to using the mixed integer programming as the usage methodology. The decision variables values of the mathematical model are computed by Lingo 17.0 optimization software. Optimization process deliver result of cost reduction of every well intervention average cost of 3.59% or about US$ 8,518."

"Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this monograph is on the identification of arrangements, which are then further restricted to where the combinatorial search is carried out by a recursive optimization process based on the general principles of dynamic programming (DP). The authors provide a comprehensive and self-contained review delineating a very general DP paradigm or schema that can serve two functions. First, the paradigm can be applied in various special forms to encompass all previously proposed applications suggested in the classification literature. Second, the paradigm can lead directly to many more novel uses. An appendix is included as a user's manual for a collection of programs available as freeware. The incorporation of a wide variety of CDA tasks under one common optimization framework based on DP is one of the book's strongest points. The authors include verifiably optimal solutions to nontrivially sized problems over the array of data analysis tasks discussed."