Optimization aims at finding a unique point, a unique state, or a unique function (a sequence of points or states) that is associated with the minimum cost or maximum benefit with respect to a certain criterion, subject to constraints. Function optimization is largely based on calculus developed...
In the absence of additional constraints the solution to the unconstrained maximization problem is easy to derive using basic calculus and equals x^=c−1Σ−1α. We would like to understand the difference x∗−x^, where x∗ is the solution of (8.12), and in particular to measure ...
(3) ≤dGδ||x−y||Ev∼S[||v||](4) =dGδ||x−y|| (1) Storkes' theorem from calculus (2) 数学期望的线性性质 (3) 琴生不等式(Jensen's inequality):对于凸函数 f ,有 E[f(x)]≥f(E[x]) (4) Lipschitz continuous 经过以上证明,我们已经得到来Lemma 2.6 的前两个性质,接下来...
The methods used in optimization vary depending on the type of problem and the variables involved. Optimization problems with discrete variables are known as combinatorial optimization problems. If the variables in the problem are continuous, we can use calculus to solve the problem....
Applied Optimization(共18册),这套丛书还有 《Inverse and Crack Identification Problems in Engineering Mechanics》《Mathematical Methods on Optimization in Transportation Systems》《Mathematical and Computational Models for Congestion Charging》《Reformulation》《Supply Chain Optimisation》等。 喜欢读"Introductory ...
Basic inequalities, such as the Hölder inequality, Minkowski inequalities, and the weighted mean inequality, etc., concerning mixed versions of discrete and continuous models, are established. By these newly formed inequalities, abundant optimization problems can be readily solved....
(Pontryagin et al., 1962;Fan and Wang, 1964;Lee and Marcus, 1967;Leitman, 1981;Sieniutycz, 1978;Findeisen et al., 1980,Sieniutycz and Jeżowski, 2018). These methods are complemented by the classical methods ofdifferential calculus,Lagrange multipliers, and thecalculus of variations(...
机器学习应用中稀疏和低秩矩阵优化的进展 Advances in Sparse and Low Rank Matrix Optimization for Machine Learning Applications 热度: Sparse autoencoder:稀疏自编码 热度: Sparse Linear Models:稀疏线性模型 热度: 相关推荐 Sparse Optimization Lecture: Basic Sparse Optimization Models Instructor: Wotao Yin...
The chapters are self-contained with basic concepts and formulations along with applications and examples. The book will be useful to researchers in engineering and mathematics, in particular those who employ computationally heavy simulations in their design work....
This page intentionally left blank ContentsPreface xviiOverview xxi1 Optimization Without Calculus 11.1 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . 11.2 The Arithmetic Mean-Geometric Mean Inequality . . . . 21.3 Applying the AGM Inequality: the Number e . . ....