Optimi Books
Shameka Roessler
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This book presents a framework for development, optimization, and evaluation of behavioral, biobehavioral, and biomedical interventions. Behavioral, biobehavioral, and biomedical interventions are programs with the objective of improving and maintaining human health and well-being, broadly defined, in individuals, families, schools, organizations, or communities. These interventions may be aimed at, for example, preventing or treating disease, promoting physical and mental health, preventing violence, or improving academic achievement.
This volume introduces the multiphase optimization strategy (MOST), pioneered at The Methodology Center at the Pennsylvania State University, as an alternative to the classical approach of relying solely on the randomized controlled trial (RCT). MOST borrows heavily from perspectives taken and approaches used in engineering, and also integrates concepts from statistics and behavioral science, including the RCT. As described in detail in this book, MOST consists of three phases: preparation, in which the conceptual model underlying the intervention is articulated; optimization, in which experimentation is used to gather the information necessary to identify the optimized intervention; and evaluation, in which the optimized intervention is evaluated in a standard RCT. Through numerous examples, the book demonstrates that MOST can be used to develop interventions that are more effective, efficient, economical, and scalable.
Optimization of Behavioral, Biobehavioral, and Biomedical Interventions: The Multiphase Optimization Strategy is the first book to present a comprehensive introduction to MOST. It will be an essential resource for behavioral, biobehavioral, and biomedical scientists; statisticians, biostatisticians, and analysts working in epidemiology and public health; and graduate-level courses in development and evaluation of interventions.
Optimization has continued to expand in all directions at anastonishing rate. New algorithmic and theoretical techniques are continuallydeveloping and the diffusion into other disciplines is proceeding at a rapidpace, with a spot light on machine learning, artificial intelligence, andquantum computing. Our knowledge of all aspects of the field has grown evenmore profound. At the same time, one of the most striking trends inoptimization is the constantly increasing emphasis on the interdisciplinary natureof the field. Optimization has been a basic tool in areas not limited toapplied mathematics, engineering, medicine, economics, computer science,operations research, and other sciences.
Remember when an optimized website was one that merely didn't take all day to appear? Times have changed. Today, website optimization can spell the difference between enterprise success and failure, and it takes a lot more know-how to achieve success.
This book is a comprehensive guide to the tips, techniques, secrets, standards, and methods of website optimization. From increasing site traffic to maximizing leads, from revving up responsiveness to increasing navigability, from prospect retention to closing more sales, the world of 21st century website optimization is explored, exemplified and explained.
Website Optimization combines the disciplines of online marketing and site performance tuning to attain the competitive advantage necessary on today's Web. You'll learn how to improve your online marketing with effective paid and natural search engine visibility strategies, strengthened lead creation and conversion to sales methods, and gold-standard ad copywriting guidelines. Plus, your increased site speed, reduced download footprint, improved reliability, and improved navigability will work synergistically with those marketing methods to optimize your site's total effectiveness.
Website Optimization not only provides you with a strategy for success, it also offers specific techniques for you and your staff to follow. A profitable website needs to be well designed, current, highly responsive, and optimally persuasive if you're to attract prospects, convert them to buyers, and get them to come back for more. This book describes precisely what you need to accomplish to achieve all of those goals.
This book offers a technical background to the design and optimization of wireless communication systems, covering optimization algorithms for wireless and 5G communication systems design. The book introduces the design and optimization systems which target capacity, latency, and connection density; including Enhanced Mobile Broadband Communication (eMBB), Ultra-Reliable and Low Latency Communication (URLL), and Massive Machine Type Communication (mMTC).
The book is organized into two distinct parts: Part I, mathematical methods and optimization algorithms for wireless communications are introduced, providing the reader with the required mathematical background. In Part II, 5G communication systems are designed and optimized using the mathematical methods and optimization algorithms.
I've argued that optimal control is a powerful framework for specifying complex behaviors with simple objective functions, letting the dynamics and constraints on the system shape the resulting feedback controller (and vice versa!). But the computational tools that we've provided so far have been limited in some important ways. The numerical approaches to dynamic programming which involve putting a mesh over the state space do not scale well to systems with state dimension more than four or five. Linearization around a nominal operating point (or trajectory) allowed us to solve for locally optimal control policies (e.g. using LQR) for even very high-dimensional systems, but the effectiveness of the resulting controllers is limited to the region of state space where the linearization is a good approximation of the nonlinear dynamics. The computational tools for Lyapunov analysis from the last chapter can provide, among other things, an effective way to compute estimates of those regions, and the sums-of-squares approaches to dynamic programming are still in their early days. We have not yet provided the mainstream computational tools for approximate optimal control that work for high-dimensional systems beyond the linearization around a goal. That is precisely the goal for this chapter.
In order to scale to high-dimensional systems, we are going to formulate a simpler version of the optimization problem. Rather than trying to solve for the optimal feedback controller for the entire state space, in this chapter we will instead attempt to find an optimal control solution that is valid from only a single initial condition. Instead of representing this as a feedback control function, we can represent this solution as a trajectory, $\bx(t), \bu(t)$, typically defined over a finite interval.
As written, the optimization above is an optimization over continuous trajectories. In order to formulate this as a numerical optimization, we must parameterize it with a finite set of numbers. Perhaps not surprisingly, there are many different ways to write down this parameterization, with a variety of different properties in terms of speed, robustness, and accuracy of the results. We will outline just a few of the most popular below; I would recommend Betts98+Betts01 for additional details.
It is worth contrasting this parameterization problem with the one that we faced in our continuous-dynamic programming algorithms. For trajectory optimization, we need a finite-dimensional parameterization in only one dimension (time), whereas in the mesh-based value iteration algorithms we had to work in the dimension of the state space. Our mesh-based discretizations scaled badly with this state dimension, and led to numerical errors that were difficult to deal with. Discreting over just one dimension (time), is fundamentally different. There is relatively much more known about discretizing solutions to differential equations over time, including work on error-controlled integration. And the number of parameters required for trajectory parameterizations scales linearly with the state dimension, instead of exponentially in mesh-based value iteration.
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