| This book provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects—modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. Two important goals of this book are to present linear and nonlinear optimization in an integrated setting, and to incorporate up-to-date interior-point methods in linear and nonlinear optimization.
As an illustration of this unified approach, almost every algorithm in this book is presented in the form of a General Optimization Algorithm. This algorithm has two major steps: an optimality test, and a step that improves the estimate of the solution. This framework is general enough to encompass the simplex method and various interior-point methods for linear programming, as well as Newton’s method and active-set methods for nonlinear optimization. The optimality test in this algorithm motivates the discussion of optimality conditions for a variety of problems. The step procedure motivates the discussion of feasible directions (for constrained problems) and Newton’s method and its variants (for nonlinear problems). |
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