Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Optimization : theory and practice

Abstract: 1. Introduction: Examples of Optimization Problems, Historical Overview.- 2. Optimality Conditions: Convex Sets, Inequalities, Local First- and Second-Order Optimality Conditions, Duality.- 3. Unconstrained Optimization Problems: Elementary Search and Localization Methods, Descent Methods with Line Search, Trust Region Methods, Conjugate Gradient Methods, Quasi-Newton Methods.- 4. Linearly Constrained Optimization Problems: Linear and Quadratic Optimization, Projection Methods.- 5. Nonlinearly Constrained Optimization Methods: Penalty Methods, SQP Methods.- 6. Interior-Point Methods for Linear Optimization: The Central Path, Newton's Method for the Primal-Dual System, Path-Following Algorithms, Predictor-Corrector Methods.- 7. Semidefinite Optimization: Selected Special Cases, The S-Procedure, The Function log det, Path-Following Methods, How to Solve SDO Problems?, Icing on the Cake: Pattern Separation via Ellipsoids.- 8. Global Optimization: Branch and Bound Methods, Cutting Plane Methods.- Appendices: A Second Look at the Constraint Qualifications, The Fritz John Condition, Optimization Software Tools for Teaching and Learning.- Bibliography.- Index of Symbols.- Subject Index.

Optimization of Models

Abstract: Designing is a complex human process that has resisted comprehensive description and understanding. All artifacts surrounding us are the results of designing. Creating these artifacts involves making a great many decisions, which suggests that designing can be viewed as a decision-making process. In the decision-making paradigm of the design process we examine the intended artifact in order to identify possible alternatives and select the most suitable one. An abstract description of the artifact using mathematical expressions of relevant natural laws, experience, collected data, and geometry is the mathematical model of the artifact. This mathematical model may contain many alternative designs, and so criteria for comparing these alternatives must be introduced in the model. Within the limitations of such a model, the best, or optimum, design can be identiied with the aid of mathematical methods. In this irst chapter we deine the design optimization problem and describe most of the properties and issues that occupy the rest of the book. We outline the limitations of our approach and caution that an " optimum " design should be perceived as such only within the scope of the mathematical model describing it and the inevitable subjective judgment of the modeler. 1.1 Mathematical Modeling Although this book is concerned with design, almost all the concepts and results described can be generalized by replacing the word design by the word system. We will then start by discussing mathematical models for general systems. The System Concept A system may be deined as a collection of entities that perform a speciied set of tasks. For example, an automobile is a system that transports passengers. It follows that a system performs a function, or process, which results in an output.It is implicit that a system operates under causality; that is, the speciied set of tasks

Models for simulation and discrete control of manufacturing systems

Abstract: A methodology is presented for constructing models of manufacturing processes for simulation and design of the discrete control logic. The models represent the discrete event evolution of the system as well as features of the underlying continuous processes. For applications such as discrete parts manufacture and assembly, the process is decomposed into operations with specified precedence relations. For each operation the required resources and associated discrete resource states are identified. Also associated with each resource is a set of resource attributes which are modified by the processes underlying each operation. The structure of the discrete-level control is modeled by modified Petri nets which are synthesized from single resource activity cycles. Construction of the net provides discrete control logic for error recovery loops and other real-time decision structures with guaranteed properties based on extensions of previous results in Petri net theory. The modeling methodology is applied to a two-arm robotic assembly cell example.