This paper considers a one-stage stochastic mathematical program with a complementarity constraint (SMPCC) where uncertainties appear in both the objective function and the complementarity constraint, and an optimal decision on both upper and lower level decision variables must be made before the realization of the uncertainties. A partially exactly penalized sample average approximation (SAA) ...

Many network optimization problems can be formulated as stochastic network design problems in which edges are present or absent stochastically. Furthermore, protective actions can guarantee that edges will remain present. We consider the problem of finding the optimal protection strategy under a budget limit in order to maximize some connectivity measurements of the network. Previous approaches...

Quantity discount is a frequently adopted scheme that has not been explicitly investigated in logistics service procurement auctions. This paper focuses on revised winner determination problem under quantity discounts and demand uncertainty for fourth-party (4PL) provider combinatorial reverse auction. To characterize our research problem, two-stage stochastic nonlinear programming model constr...

In rare situations, stochastic programs can be solved analytically. Otherwise, approximation is necessary to solve stochastic programs with a large or infinite number of scenarios to a desired level of accuracy. This involves statistical sampling or deterministic selection of a finite set of scenarios to obtain a tractable deterministic equivalent problem. Some of these approaches rely on bound...

Abstract This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing problem in a stochastic optimization setting. By doing so, we show that many are variants sample average approximation (SAA). More importantly, able to prove single theoretical result guarantees asymptotic convergence variety methods. Additional...

The wide spread of district heating in Denmark offers a massive potential for flexibility an energy system with intermittent renewable production. To leverage this potential, cost-efficient power market integration combined heat and (CHP) units systems is important. We propose stochastic program optimising block bids to the day-ahead CHP under uncertain prices. Block allow internalisation start...

The mathematical modelling of the polarized radiation transfer (RT) at the satellite remote sensing (SRS) of the strongly anisotropic cloudy atmosphere needs an efficient well-conditioned algorithm with accelerated solution convergence to be developed. The accelerated convergence can be achieved by the small angle approximation (SAA) subtracting from the general solution of the vectorial (polar...

We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are “sub-Gaussian” even when randomness problem is fairly heavy tailed. Additionally, we obtain good (often optimal) dependence on size geometrical parameters Finally, allow random constraints SAA unbounded ...

Scheduling-Location (ScheLoc) problem considering machine location and job scheduling simultaneously is a relatively new hot topic. The existing works assume that only one can be placed at location, which may not suitable for some practical applications. Besides, the customer credit risk largely impacts manufacturer’s profit has been addressed in ScheLoc problem. Therefore, this work, we study ...

We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., problems in which there are first-stage feasible solutions that not guaranteed to have a recourse action. As feasibility measure of the SAA solution, we consider "recourse likelihood", is probability solution has For $\epsilon \in (0,1)$, demonstrate likelihood below $...