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Abstrak :
Tugas Akhir ini membahas suatu metode penyelesaian masalah pemrograman linier dengan menggunakan Algoritma Interior-Point. Algoritma ini didasarkan pada model pemrograman linier yang memaksimumkan fungsi tujuan. DimuIai dengan memilih sembarang titik-dalam pada daerah layak sebagai penyelesaian awal, lalu variabel-variabel keputusan yang ada dalam model diubah skalanya, sehingga diperoleh penyelesaian awal yang konstan ( 1, 1, 1, . . , 1 ). Kemudian algoritma dilanjutkan dengan menghitung matriks proyeksi ( P ) dan menetapkan nilai a untuk mendapatkan arah gerakan dari titik penyelesaian awal. Algoritma diakhiri dengan menghitung titik penyelesaian awal berikutnya. Dengan melakukan iterasi akan diperoleh titik optimal yang ditandai dengan tidak berubahnya titik yang diperoleh pada akhir iterasi.

Abstrak :
Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs. The book contains new and important results in the general theory of convex programming, e.g., their "conic" problem formulation in which duality theory is completely symmetric. For each algorithm described, the authors carefully derive precise bounds on the computational effort required to solve a given family of problems to a given precision. In several cases they obtain better problem complexity estimates than were previously known. Several of the new algorithms described in this book, e.g., the projective method, have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.

Abstrak :
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.

Abstrak :
In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.

Abstrak :
This paper provides a developed mathematical model to derive the optimal integrated lot sizing in a multi-level supply chain with imperfect quality products. The developed mathematical model has a bi-objective function, with conflicting goals, minimizing the chain inventory costs and maximizing the chain total profit aided to find optimum policy for integrated lot sizing. We further actualize the problem by assuming multiple stochastic constraints. The mathematical formulation of the problem is stochastic, nonlinear, and large. In this regard, the interior point algorithm that is developed as more effective algorithm with less iteration is used for solving the recent convex nonlinear model. Numerical example shows that the developed interior point method is an efficient method with excellent performance in terms of the quality of the solution. Also, Sensitivity analysis shows that the developed interior point method is an efficient method with excellent performance in terms of the quality of the solution.

Abstrak :
The thesis focuses on the control of blood glucose devices and design of implantable devices, and offers valuable insights on diabetes mellitus and related physiology and treatments. Diabetes mellitus is a widespread chronic disease in the modern world that affects millions of people around the globe. In Singapore, one in ten of the population has diabetes, and the severity of the problem has prompted the country’s prime minister to talk about the disease at the National Day Rally in 2017. Designing an artificial pancreas that can provide effective blood glucose control for individuals with diabetes is one of the most challenging engineering problems. The author reports on research into the development of an implantable artificial pancreas that can regulate blood glucose levels by delivering appropriate dosages of insulin when necessary. By sensing blood glucose and injecting insulin directly into the vein, the implantable device aims to remove delays that occur with subcutaneous blood glucose sensing and insulin delivery. Preliminary in-vitro and in-vivo experimental results suggest that the implantable device for blood glucose control could be a clinically viable alternative to pancreas transplant.