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In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...
This work aims to study the effects of wind uncertainties in civil engineering structural design. Optimising the design of a structure for safety or operability without factoring in these uncertainties can result in a design that is not robust to these per ...
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...
2022
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We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained t ...
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a sig ...
TAYLOR & FRANCIS LTD2022
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Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...
It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker's p ...
We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...
We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...
Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor loc ...
