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* {{le|隨機梯度下降法|Stochastic gradient descent}} * {{cite book | year=1997 | title=Optimization : Algorithms and Consistent Approximations | publisher=Springer-Verlag | is …

| title = The common source of several inequalities concerning doubly stochastic matrices …tle = Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix …

…是一種求解{{link-en|強健最佳化|robust optimization}}問題和[[機會約束規劃]]（chance-constrained optimization）問題的方式，其方法會以一些[[約束 (數學)|約束]]的樣本為基礎。情境最佳化也和建模及決策中的[[归纳推理]]有關。此方法已以[[启发法]]的形式存 …ibility of Randomized Solutions of Uncertain Convex Programs.'' SIAM J. on Optimization, 19, no.3: 1211–1230, 2008.[http://epubs.siam.org/siopt/resource/1/sj …

* {{le|随机梯度下降法|Stochastic gradient descent}} …an (2005). ''Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms.'' Springer Publish …

…lls. Effect of Rounding errors on the Variable Metric Method. ''Journal of Optimization Theory and Applications'' '''80''', 1994. [http://portal.acm.org/citation.c …羅森布羅克函數延伸到隨機（stochastic）函數，以下是一種例子：<ref>Yang X.-S. and Deb S., Engineering optimization by cuckoo searc１h, Int. J. Math. Modelling Num. Optimisation, Vol. 1, No.… …

…前提下最大化仿真效率。<ref>Fu, M, C. H. Chen, and L. Shi, “Some Topics for Simulation Optimization,” Proceedings of 2008 Winter Simulation Conference, pp. 27–38, Miami, FL,… …或）所需的仿真时间，以达到可接受的（或最好的）结果。<ref>Chen, and Loo H. Lee. Stochastic simulation optimization an optimal computing budget allocation. Singapore Hackensack, NJ: World Sci …

….springer.com/content/pdf/10.1007%2F978-3-030-05318-5_1.pdf Hyperparameter optimization] {{Wayback|url=https://link.springer.com/content/pdf/10.1007%2F978-3-030-05 …st2=Bengio|first2=Yoshua|year=2012|title=Random Search for Hyper-Parameter Optimization|url=http://jmlr.csail.mit.edu/papers/volume13/bergstra12a/bergstra12a.pdf|j …

…y Optimization，TRPO）<ref name="schulman2015trpo"/>、近端策略最佳化（Proximal Policy Optimization，PPO）<ref name="schulman2017ppo"/>。另一系列的無模型深度強化學習演算法則是訓練類神經網路模型來預測未來的獎勵總和 <m <ref name="schulman2015trpo">{{Cite conference|title=Trust Region Policy Optimization|last1=Schulman|first1=John|last2=Levine|first2=Sergey|last3=Moritz|first3=P …

| presenter = {{en-link|国际数学优化学会|Mathematical Optimization Society}}<br />[[美国数学学会]] '''富尔克森奖'''（{{lang-en|Fulkerson Prize}}）是{{en-link|国际数学优化学会|Mathematical Optimization Society}}和[[美国数学学会]]联合设立的奖项，专门奖励[[离散数学]]领域的杰出论文。在国际数学优化学会每三年召开一次的大会上奖励至多三篇论 …

…ast=Kamien, Morton I.|url=http://worldcat.org/oclc/869522905|title=Dynamic Optimization : the Calculus of Variations and Optimal Control in Economics and Managemen …allel optimization in astrodynamics (the case of interplanetary trajectory optimization)." Proceed. Fifth International Conf. Astrodynam. Tools and Techniques, ICA …

…itsenhausen}}在1968年所提出的[[反例]]<ref>Witsenhausen, Hans. "A counterexample in stochastic optimum control." ''SIAM J. Control'', Volume 6, Issue 1, pp. 131–147 (Febr …Witsenhausen counterexample: A hierarchical search approach for nonconvex optimization problems." '' IEEE Trans. Automatic Control'', 2001</ref>，Li, Marden和{{link …

…r-first=C. |editor2-last=Pardalos |editor2-first=P. |title=Encyclopedia of Optimization |publisher=Springer |location=Boston |pages=1538–1542 }}</ref> …www.dictionaryofeconomics.com/article?id=pde2008_A000133&edition=current&q=optimization&topicid=&result_number=20 |date=20170811183914 }}" by [[John Geanakoplos]]. …

…author-link=Pat Moran (statistician) |year=1950 |title=Notes on Continuous Stochastic Phenomena |journal=Biometrika |volume=37 |issue=1 |page=17–23 |doi=10.2307/ …lineation of geomorphological slope units with r.slopeunits v1.0 and their optimization for landslide susceptibility modeling |journal=Geoscientific Model Developm …

…-Carlo Method for the Approximate Solution of Certain Types of Constrained Optimization Problems|journal=Journal of the Operations Research Society of America|volu …985-01_45_1/page/41 |year=1985 |last1=Černý |first1=V. |journal=Journal of Optimization Theory and Applications |volume=45 |pages=41–51|s2cid=122729427 }}</ref>这种方 …

…rs | first2 = J. | date = 2010 | doi = 10.1007/s11004-010-9276-7 | title = Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling |journal=[[Mat …ch |title=Learning with Kernels : Support Vector Machines, Regularization, Optimization, and Beyond |publisher=MIT Press |year=2018 |isbn=978-0-262-53657-8 |url=ht …

#''Brownian Motion and Stochastic Calculus'', Ioannis Karatzas, [[Steven E. Shreve|Steven Shreve]] (2ed 2000, #''Foundations of Optimization in Finite Dimensions'', [[Osman Guler]], (2010, {{ISBN|978-0-387-34431-7}}) …

通过求解上述问题的{{le|对偶 (最优化)|Duality (optimization)|拉格朗日对偶}}，得到简化的问题<blockquote><math> \text{maximize}\,\, f(c_1 \ldots c_n)… …\vec w</math> 与 <math>b</math> 的[[凸函数]]。因此，可以采用传统的[[梯度下降法|梯度下降]]（或{{tsl|en|Stochastic gradient descent||SGD}}）方法，其中不是在函数梯度的方向上前进，而是在从函数的[[次导数|次梯度]]中选出的向量的方向上前进。该 …

…rank J. |title=Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures |isbn=978-0-470-0531 …

…name="Ekeland76"/><ref name="Bertsekas82"/>概率論中，引理適用於[[數學證明|證明]]{{Le|隨機幾何|Stochastic geometry|隨機集}}的「[[大數法則|大數定律]]」。此定理先前僅在凸集的情況得證。<ref name="ArtsteinVitale">{{ | title = Convex Optimization Theory …

…ebst.pdf|dead-url=no}}</ref><ref name="Friedman1999b">{{Cite journal|title=Stochastic Gradient Boosting|url=https://statweb.stanford.edu/~jhf/ftp/stobst.pdf|last …plier <math>\gamma_m</math> by solving the following [[线搜索|one-dimensional optimization]] problem: …