Related papers: Minimizing risk measures with applications in netw…
This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
Effective risk monitoring in dynamic environments such as disaster zones requires an adaptive exploration strategy to detect hidden threats. We propose a bi-level unmanned aerial vehicle (UAV) monitoring strategy that efficiently integrates…
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
This paper introduces a local planner that synergizes the decision making and trajectory planning modules towards autonomous driving. The decision making and trajectory planning tasks are jointly formulated as a nonlinear programming…
In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
Conditional Value-at-Risk (CVaR) is a leading tail-risk measure in finance, central to both regulatory and portfolio optimization frameworks. Classical estimation of CVaR and its gradients relies on Monte Carlo simulation, incurring…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…
Vehicle trajectory optimization is essential to ensure vehicles travel efficiently and safely. This paper presents an infrastructure assisted constrained connected automated vehicles (CAVs) trajectory optimization method on curved roads.…
We present the conditional value-at-risk (CVaR) in the context of Markov chains and Markov decision processes with reachability and mean-payoff objectives. CVaR quantifies risk by means of the expectation of the worst p-quantile. As such it…
This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal…
The increasing integration of intermittent distributed energy resources (DERs) has introduced significant variability in distribution networks, posing challenges to voltage regulation and reactive power management. This paper presents a…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient…