Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Parallel processors for planning under uncertainty
Annals of Operations Research
Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Annals of Operations Research - Special issue on sensitivity analysis and optimization of discrete event systems
Inexact subgradient methods with applications in stochastic programming
Mathematical Programming: Series A and B
Analysis of sample-path optimization
Mathematics of Operations Research
A simulation-based approach to two-stage stochastic programming with recourse
Mathematical Programming: Series A and B
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Inexact Cuts in Benders Decomposition
SIAM Journal on Optimization
Decomposition Algorithms for Stochastic Programming on a Computational Grid
Computational Optimization and Applications
A multistage stochastic programming algorithm suitable for parallel computing
Parallel Computing - Special issue: Parallel computing in numerical optimization
Variable-sample methods for stochastic optimization
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Sequential quadratic programming methods based on indefinite hessian approximations
Sequential quadratic programming methods based on indefinite hessian approximations
A Decomposition Method Based on SQP for a Class of Multistage Stochastic Nonlinear Programs
SIAM Journal on Optimization
A Lagrangian Dual Method with Self-Concordant Barriers for Multi-Stage Stochastic Convex Programming
Mathematical Programming: Series A and B
Expected Residual Minimization Method for Stochastic Linear Complementarity Problems
Mathematics of Operations Research
Robust solution of monotone stochastic linear complementarity problems
Mathematical Programming: Series A and B
Variable-Number Sample-Path Optimization
Mathematical Programming: Series A and B
A Complementarity Framework for Forward Contracting Under Uncertainty
Operations Research
Automatica (Journal of IFAC)
On stochastic gradient and subgradient methods with adaptive steplength sequences
Automatica (Journal of IFAC)
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In this paper, we study recourse-based stochastic nonlinear programs and make two sets of contributions. The first set assumes general probability spaces and provides a deeper understanding of feasibility and recourse in stochastic nonlinear programs. A sufficient condition, for equality between the sets of feasible first-stage decisions arising from two different interpretations of almost sure feasibility, is provided. This condition is an extension to nonlinear settings of the "W-condition," first suggested by Walkup and Wets (SIAM J. Appl. Math. 15:1299---1314, 1967). Notions of complete and relatively-complete recourse for nonlinear stochastic programs are defined and simple sufficient conditions for these to hold are given. Implications of these results on the L-shaped method are discussed. Our second set of contributions lies in the construction of a scalable, superlinearly convergent method for solving this class of problems, under the setting of a finite sample-space. We present a novel hybrid algorithm that combines sequential quadratic programming (SQP) and Benders decomposition. In this framework, the resulting quadratic programming approximations while arbitrarily large, are observed to be two-period stochastic quadratic programs (QPs) and are solved through two variants of Benders decomposition. The first is based on an inexact-cut L-shaped method for stochastic quadratic programming while the second is a quadratic extension to a trust-region method suggested by Linderoth and Wright (Comput. Optim. Appl. 24:207---250, 2003). Obtaining Lagrange multiplier estimates in this framework poses a unique challenge and are shown to be cheaply obtainable through the solution of a single low-dimensional QP. Globalization of the method is achieved through a parallelizable linesearch procedure. Finally, the efficiency and scalability of the algorithm are demonstrated on a set of stochastic nonlinear programming test problems.