Saddle point approximation approaches for two-stage robust optimization problems

2019 ◽  
Vol 78 (4) ◽  
pp. 651-670
Author(s):  
Ning Zhang ◽  
Chang Fang
Keyword(s):  
Robust Optimization ◽  
Saddle Point ◽  
Optimization Problems ◽  
Saddle Point Approximation ◽  
Two Stage ◽  
Point Approximation

scholarly journals Oracle-based algorithms for binary two-stage robust optimization

2020 ◽  
Vol 77 (2) ◽  
pp. 539-569
Author(s):  
Nicolas Kämmerling ◽  
Jannis Kurtz
Keyword(s):  
Robust Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Capital Budgeting ◽  
Hub Location Problem ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Problem ◽  
Objective Uncertainty

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

2020 ◽  
Author(s):  
Amir Ardestani-Jaafari ◽  
Erick Delage
Keyword(s):  
Robust Optimization ◽  
Operations Management ◽  
Optimization Problems ◽  
Close Relation ◽  
Bilinear Programming ◽  
Two Stage ◽  
Bilinear Models ◽  
Robust Counterpart ◽  
Adjustable Robust Counterpart ◽  
Affinely Adjustable Robust Counterpart

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

Time-Dependent Kinematic Reliability Analysis of Gear Mechanism Based on Sequential Decoupling Strategy and Saddle-Point Approximation

2021 ◽  
pp. 108292
Author(s):  
Junhua Chen ◽  
Longmiao Chen ◽  
Linfang Qian ◽  
Guangsong Chen ◽  
Shijie Zhou
Keyword(s):  
Saddle Point ◽  
Reliability Analysis ◽  
Time Dependent ◽  
Saddle Point Approximation ◽  
Point Approximation ◽  
Gear Mechanism

scholarly journals Polymer quantization and the saddle point approximation of partition functions

2015 ◽  
Vol 92 (10) ◽  
Author(s):  
Hugo A. Morales-Técotl ◽  
Daniel H. Orozco-Borunda ◽  
Saeed Rastgoo
Keyword(s):  
Saddle Point ◽  
Partition Functions ◽  
Saddle Point Approximation ◽  
Point Approximation

Performance evaluation of optical DQPSK using saddle point approximation

2006 ◽  
Vol 24 (3) ◽  
pp. 1176-1185 ◽  
Author(s):  
N.S. Avlonitis ◽  
E.M. Yeatman
Keyword(s):  
Performance Evaluation ◽  
Saddle Point ◽  
Saddle Point Approximation ◽  
Point Approximation

scholarly journals K-adaptability in two-stage mixed-integer robust optimization

2019 ◽  
Vol 12 (2) ◽  
pp. 193-224 ◽  
Author(s):  
Anirudh Subramanyam ◽  
Chrysanthos E. Gounaris ◽  
Wolfram Wiesemann
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Finite Convergence ◽  
Two Stage ◽  
Infinite Dimensional ◽  
Benchmark Data ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation

Abstract We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying a K-adaptability formulation that selects K candidate recourse policies before observing the realization of the uncertain parameters and that implements the best of these policies after the realization is known. We address the second challenge through a branch-and-bound scheme that enjoys asymptotic convergence in general and finite convergence under specific conditions. We illustrate the performance of our algorithm in numerical experiments involving benchmark data from several application domains.

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