Related papers: Two-stage Stochastic Programming under Multivariat…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
The frequency of wildfire disasters has surged five-fold in the past 50 years due to climate change. Preemptive de-energization is a potent strategy to mitigate wildfire risks but substantially impacts customers. We propose a multistage…
The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
We consider the problem of preparing for a disaster season by determining where to open warehouses and how much relief item inventory to preposition in each. Then, after each disaster, prepositioned items are distributed to demand nodes…
We address multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot…
Two-stage stochastic linear optimization is known to be #P-hard when all involved random variables are independently and uniformly distributed over intervals, even with fixed recourse. We show that this problem is actually #P-hard in the…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…
Assemble-to-order approaches deal with randomness in demand for end items by producing components under uncertainty, but assembling them only after demand is observed. Such planning problems can be tackled by stochastic programming, but…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
Mobility systems featuring shared vehicles are often unable to serve all potential customers, as the distribution of demand does not coincide with the positions of vehicles at any given time. System operators often choose to reposition…
A multilevel network is defined as the junction of two interaction networks, one level representing the interactions between individuals and the other the interactions between organizations. The levels are linked by an affiliation…
Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic…
Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…
In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a…