Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as...
Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the hear...
In this book the authors take a rigorous look at the infinite-horizon discrete-time optimal control theory from the viewpoint of Pontryagin's principles. Several Pontryagin principles are described which govern systems and various criteria which define the notions of optimality, along with a detailed analysis of how each Pontryagin principle relate to each other. The Pontryagin principle is examined in a stochastic setting and results are given which generalize Pontryagin's principles to multi-criteria problems. Infinite-Horizon Optimal Control in the...
In this book the authors take a rigorous look at the infinite-horizon discrete-time optimal control theory from the viewpo...
Optimization Approaches for Solving String Selection Problems provides an overview of optimization methods for a wide class of genomics-related problems in relation to the string selection problems. This class of problems addresses the recognition of similar characteristics or differences within biological sequences. Specifically, this book considers a large class of problems, ranging from the closest string and substring problems, to the farthest string and substring problems, to the far from most string problem. Each problem includes a detailed description, highlighting both...
Optimization Approaches for Solving String Selection Problems provides an overview of optimization methods for a wide class of genomics-rela...
Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on...
Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into th...
Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line. Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations are illustrated throughout this book. This book also contains significant results and information...
Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of v...
Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in...
Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage o...
This title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of optimal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any...
This title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the ...
Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given...
Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: model...
This Brief reviews a number of techniques exploiting the surrogate-based optimization concept and variable-fidelity EM simulations for efficient optimization of antenna structures. The introduction of each method is illustrated with examples of antenna design. The authors demonstrate the ways in which practitioners can obtain an optimized antenna design at the computational cost corresponding to a few high-fidelity EM simulations of the antenna structure. There is also a discussion of the selection of antenna model fidelity and its influence on performance of the surrogate-based design...
This Brief reviews a number of techniques exploiting the surrogate-based optimization concept and variable-fidelity EM simulations for efficient optim...
This book results from a long-term research effort aimed at tackling complex non-standard packing issues which arise in space engineering. The main research objective is to optimize cargo loading and arrangement, in compliance with a set of stringent rules. Complicated geometrical aspects are also taken into account, in addition to balancing conditions based on attitude control specifications.
Chapter 1 introduces the class of non-standard packing problems studied. Chapter 2 gives a detailed explanation of a general model for the orthogonal packing of tetris-like items in a convex...
This book results from a long-term research effort aimed at tackling complex non-standard packing issues which arise in space engineering. The main...
