Methods of Dynamic and Nonsmooth Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Dynamic and Nonsmooth Optimization write by Frank H. Clarke. This book was released on 1989-01-01. Methods of Dynamic and Nonsmooth Optimization available in PDF, EPUB and Kindle. 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. 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.
Methods of Dynamic and Nonsmooth Optimization
Methods of Dynamic and Nonsmooth Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Dynamic and Nonsmooth Optimization write by Frank H. Clarke. This book was released on 1989-01-01. Methods of Dynamic and Nonsmooth Optimization available in PDF, EPUB and Kindle. 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.
Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control
Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control write by Marko M Makela. This book was released on 1992-05-07. Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control available in PDF, EPUB and Kindle. This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.
Nonsmooth Dynamic Optimization of Systems with Varying Structure
Nonsmooth Dynamic Optimization of Systems with Varying Structure - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Dynamic Optimization of Systems with Varying Structure write by Mehmet Yunt. This book was released on 2011. Nonsmooth Dynamic Optimization of Systems with Varying Structure available in PDF, EPUB and Kindle. In this thesis, an open-loop numerical dynamic optimization method for a class of dynamic systems is developed. The structure of the governing equations of the systems under consideration change depending on the values of the states, parameters and the controls. Therefore, these systems are called systems with varying structure. Such systems occur frequently in the models of electric and hydraulic circuits, chemical processes, biological networks and machinery. As a result, the determination of parameters and controls resulting in the optimal performance of these systems has been an important research topic. Unlike dynamic optimization problems where the structure of the underlying system is constant, the dynamic optimization of systems with varying structure requires the determination of the optimal evolution of the system structure in time in addition to optimal parameters and controls. The underlying varying structure results in nonsmooth and discontinuous optimization problems. The nonsmooth single shooting method introduced in this thesis uses concepts from nonsmooth analysis and nonsmooth optimization to solve dynamic optimization problems involving systems with varying structure whose dynamics can be described by locally Lipschitz continuous ordinary or differential-algebraic equations. The method converts the infinitedimensional dynamic optimization problem into an nonlinear program by parameterizing the controls. Unlike the state of the art, the method does not enumerate possible structures explicitly in the optimization and it does not depend on the discretization of the dynamics. Instead, it uses a special integration algorithm to compute state trajectories and derivative information. As a result, the method produces more accurate solutions to problems where the underlying dynamics is highly nonlinear and/or stiff for less effort than the state of the art. The thesis develops substitutes for the gradient and the Jacobian of a function in case these quantities do not exist. These substitutes are set-valued maps and an elements of these maps need to be computed for optimization purposes. Differential equations are derived whose solutions furnish the necessary elements. These differential equations have discontinuities in time. A numerical method for their solution is proposed based on state event location algorithms that detects these discontinuities. Necessary conditions of optimality for nonlinear programs are derived using these substitutes and it is shown that nonsmooth optimization methods called bundle methods can be used to obtain solutions satisfying these necessary conditions. Case studies compare the method to the state of the art and investigate its complexity empirically.
Introduction to Nonsmooth Optimization
Introduction to Nonsmooth Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Nonsmooth Optimization write by Adil Bagirov. This book was released on 2014-08-12. Introduction to Nonsmooth Optimization available in PDF, EPUB and Kindle. This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.
