Related papers: On a robust approach to "split" feasibility proble…
In this paper we study feasibility and infeasibility of nonlinear two-stage fully adjustable robust feasibility problems with an empty first stage. This is equivalent to deciding whether the uncertainty set is contained within the…
This paper deals with a robust recoverable approach to 0-1 programming problems. It is assumed that a solution constructed in the first stage can be modified to some extent in the second stage. This modification consists in choosing a…
We study a robust extensible bin packing problem with budgeted uncertainty, under a budgeted uncertainty model where item sizes are defined to lie in the intersection of a box with a one-norm ball. We propose a scenario generation algorithm…
This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
The optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints)…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
We consider global non-convex optimisation problems under uncertainty. In this setting, it is not possible to implement a desired solution exactly. Instead, any other solution within some distance to the intended solution may be…
In this paper we discuss the existence of solutions to vectorial differential inclusions. We investigate sufficient conditions for existence, more flexible than those available in the literature, so that important applications can be fitted…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
In this paper, probabilistic guarantees for constraint sampling of multistage robust convex optimization problems are derived. The dynamic nature of these problems is tackled via the so-called scenario-with-certificates approach. This…
We study the decision version of tensor spectral norm from the viewpoint of real algebraic complexity. For a rationally specified tensor, the tensor spectral threshold problem asks whether its spectral norm exceeds a prescribed rational…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…