Cerf M. Optimization techniques I. Continuous optimization 2023 torrent

Textbook in PDF format

This book in two volumes provides an overview of continuous, discrete and functional optimization techniques. This first volume is devoted to continuous optimization, which deals with problems with real variables, without or with constraints. After a reminder of the optimality conditions and their geometrical interpretation, the topics covered are:-gradient-free algorithms that can be applied to any type of function;-unconstrained algorithms based on Newton-type descent methods;-algorithms with constraints: penalization, primal, dual and primal-dual methods;-linear programming with the simplex method and interior point methods. The emphasis is on understanding the principles rather than on mathematical rigor. Each concept or algorithm is accompanied by a detailed example to help you grasp the main ideas. This book is the result of 30 years of experience and is intended for students, researchers and engineers wishing to acquire a general knowledge in the field of optimization.
Preface
Introduction
Continuous optimization
Introduction
Formulation
Numerical derivatives
Problem reduction
Global optimum
Local optimum
Conclusion
Gradient-free optimization
Introduction
Difficult optimization
One-dimensional optimization
DIRECT method
Nelder-Mead method
Affine shaker
CMAES
Simulated annealing
Research with tabu
Particle swarms
Ant colonies
Evolutionary algorithms
Conclusion
Unconstrained optimization
Introduction
Newton’s method
Quasi-Newton methods
Line search
Trust region
Proximal methods
Convergence
Conclusion
Constrained optimization
Introduction
Classification of methods
Penalization
Reduced gradient
Sequential quadratic programming
Interior point
Augmented Lagrangian
Conclusion
Linear programming
oduction
Simplex
Interior point
Conclusion
Index
Bibliography