Related papers: Characterizations of robust and stable duality for…
In this paper we introduce a sublinear conditional expectation with respect to a family of possibly nondominated probability measures on a progressively enlarged filtration. In this way, we extend the classic reduced-form setting for credit…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables…
We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via…
Two genres of heuristics that are frequently reported to perform much better on "real-world" instances than in the worst case are greedy algorithms and local search algorithms. In this paper, we systematically study these two types of…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the…
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…
Constrained reinforcement learning is to maximize the expected reward subject to constraints on utilities/costs. However, the training environment may not be the same as the test one, due to, e.g., modeling error, adversarial attack,…
This article develops a duality principle for a class of optimization problems in $\mathbb{R}^n$. The results are obtained based on standard tools of convex analysis and on a well known result of Toland for D.C. optimization. Global…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
This paper delves into the challenging issues in uncertain multi-objective optimization, where uncertainty permeates nonsmooth nonconvex objective and constraint functions. In this context, we investigate highly robust (weakly efficient)…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…