The idea of k-adaptability in two-stage robust optimization is to calculate a fixed number k of second-stage policies here-and-now. After the actual scenario is revealed, the best of these policies is selected. This idea leads to a min-max-min problem. In this paper, we consider the case where no first stage variables exist and propose to … Read more
The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population … Read more
In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal … Read more
A key step in solving minimax distributionally robust optimization (DRO) problems is to reformulate the inner maximization w.r.t. probability measure as a semiinfinite programming problem through Lagrange dual. Slater type conditions have been widely used for zero dual gap when the ambiguity set is defined through moments. In this paper, we investigate effective ways for … Read more
In this paper, we develop a risk-averse two-stage stochastic program (RTSP) which explicitly incorporates the distributional ambiguity covering both discrete and continuous distributions. Starting from a set of historical data samples, we construct a confidence set for the ambiguous probability distribution through nonparametric statistical estimation of its density function. We then formulate RTSP from the … Read more
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of … Read more
Robust nonlinear optimization is not as well developed as the linear case, and limited in the constraints and uncertainty sets it can handle. In this work we extend the scope of robust optimization by showing how to solve a large class of robust nonlinear optimization problems. The fascinating and appealing property of our approach is … Read more
We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate second-stage policies here-and-now and implement the best of these policies once the uncertain parameters have been observed. We analyze the approximation quality and the computational complexity of the K-adaptability problem, and we derive explicit … Read more
With the introduction of new technologies like electric vehicles and smart grids the operation and planning of power systems are subject to major changes. These technologies can bring various ftexibilities to different entities involved in decision making. This paper proposes a robust optimization based method to optimal charging/discharging of electric vehicles con sidering the electricity … Read more
In this paper we consider a transportation problem under uncertainty related to gypsum replenishment for a cement producer. The problem is to determine the number of vehicles to book at the beginning of each week to replenish gypsum at all the cement factories of the producer in order to minimize the total cost, given by … Read more