Related papers: Sampling methods for multistage robust convex opti…

In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control,…

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…

In this paper, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is motivated by the observation that in many control…

In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability…

We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of…

Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…

This paper addresses a central challenge of jointly considering shorter-term (e.g. hourly) and longer-term (e.g. yearly) uncertainties in power system planning with increasing penetration of renewable and storage resources. In conventional…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time,…

Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled…

We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…

A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…

We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…

We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…

In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that,…