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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
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Journal ArticleDOI
12 Sep 1999
TL;DR: Under the framework of probabilistic optimization, this work proposes to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness.
Abstract: In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses and methods that do not. Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques under different circumstances. Under the framework of probabilistic optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry.

395 citations

Journal ArticleDOI
TL;DR: In this article, a mixed-integer linear programming model is proposed that minimizes the total cost of a closed-loop supply chain (CLSC) network consisting of both forward and reverse supply chains.

391 citations

Journal ArticleDOI
TL;DR: This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption, and provides a new solution methodology using the Moreau–Yosida regularization.

388 citations

Book
01 Jan 2007
TL;DR: In this paper, the authors present a general framework for portfolio allocation based on mean-variance analysis and modern portfolio theory, with a focus on portfolio selection with higher moments through expansions of utility functions.
Abstract: Preface. About the Authors. CHAPTER 1. Introduction. Quantitative Techniques in the Investment Management Industry. Central Themes of This Book. Overview of This Book. PART ONE. Portfolio Allocation: Classical Theory and Extensions. CHAPTER 2. Mean-Variance Analysis and Modern Portfolio Theory. The Benefits of Diversification. Mean-Variance Analysis: Overview. Classical Framework for Mean-Variance Optimization. The Capital Market Line. Selection of the Optimal Portfolio When There Is a Risk-Free Asset. More on Utility Functions: A General Framework for Portfolio Choice. Summary. CHAPTER 3. Advances in the Theory of Portfolio Risk Measures. Dispersion and Downside Measures. Portfolio Selection with Higher Moments through Expansions of Utility. Polynomial Goal Programming for Portfolio Optimization with Higher Moments. Some Remarks on the Estimation of Higher Moments. The Approach of Malevergne and Sornette. Summary. CHAPTER 4. Portfolio Selection in Practice. Portfolio Constraints Commonly Used in Practice. Incorporating Transaction Costs in Asset-Allocation Models. Multiaccount Optimization. Summary. PART TWO. Robust Parameter Estimation. CHAPTER 5. Classical Asset Pricing. Definitions. Theoretical and Econometric Models. Random Walk Models. General Equilibrium Theories. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Summary. CHAPTER 6. Forecasting Expected Return and Risk. Dividend Discount and Residual Income Valuation Models. The Sample Mean and Covariance Estimators. Random Matrices. Arbitrage Pricing Theory and Factor Models. Factor Models in Practice. Other Approaches to Volatility Estimation. Application to Investment Strategies and Proprietary Trading. Summary. CHAPTER 7. Robust Estimation. The Intuition behind Robust Statistics. Robust Statistics. Robust Estimators of Regressions. Confidence Intervals. Summary. CHAPTER 8. Robust Frameworks for Estimation: Shrinkage, Bayesian Approaches, and the Black-Litterman Model. Practical Problems Encountered in Mean-Variance Optimization. Shrinkage Estimation. Bayesian Approaches. Summary. PART THREE. Optimization Techniques. CHAPTER 9. Mathematical and Numerical Optimization. Mathematical Programming. Necessary Conditions for Optimality for Continuous Optimization Problems. Optimization Duality Theory. How Do Optimization Algorithms Work? Summary. CHAPTER 10. Optimization under Uncertainty. Stochastic Programming. Dynamic Programming. Robust Optimization. Summary. CHAPTER 11. Implementing and Solving Optimization Problems in Practice. Optimization Software. Practical Considerations When Using Optimization Software. Implementation Examples. Specialized Software for Optimization Under Uncertainty. Summary. PART FOUR. Robust Portfolio Optimization. CHAPTER 12. Robust Modeling of Uncertain Parameters in Classical Mean-Variance Portfolio Optimization. Portfolio Resampling Techniques. Robust Portfolio Allocation. Some Practical Remarks on Robust Portfolio Allocation Models. Summary. CHAPTER 13. The Practice of Robust Portfolio Management: Recent Trends and New Directions. Some Issues in Robust Asset Allocation. Portfolio Rebalancing. Understanding and Modeling Transaction Costs. Rebalancing Using an Optimizer. Summary. CHAPTER 14. Quantitative Investment Management Today and Tomorrow. Using Derivatives in Portfolio Management. Currency Management. Benchmarks. Quantitative Return-Forecasting Techniques and Model-Based Trading Strategies. Trade Execution and Algorithmic Trading. Summary. APPENDIX A. Data Description: The MSCI World Index. INDEX.

375 citations

Journal ArticleDOI
TL;DR: In this paper, a randomized stochastic projected gradient (RSPG) algorithm was proposed to solve the convex composite optimization problem, in which proper mini-batch of samples are taken at each iteration depending on the total budget of stochiastic samples allowed, and a post-optimization phase was also proposed to reduce the variance of the solutions returned by the algorithm.
Abstract: This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are taken at each iteration depending on the total budget of stochastic samples allowed. The RSPG algorithm also employs a general distance function to allow taking advantage of the geometry of the feasible region. Complexity of this algorithm is established in a unified setting, which shows nearly optimal complexity of the algorithm for convex stochastic programming. A post-optimization phase is also proposed to significantly reduce the variance of the solutions returned by the algorithm. In addition, based on the RSPG algorithm, a stochastic gradient free algorithm, which only uses the stochastic zeroth-order information, has been also discussed. Some preliminary numerical results are also provided.

375 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532