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Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…

We study episodic reinforcement learning (RL) in non-stationary linear kernel Markov decision processes (MDPs). In this setting, both the reward function and the transition kernel are linear with respect to the given feature maps and are…

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…

Robust optimization is an established framework for modeling optimization problems with uncertain parameters. While static robust optimization is often criticized for being too conservative, two-stage (or adjustable) robust optimization…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Bayesian Optimization (BO) is a common solution to search optimal hyperparameters based on sample observations of a machine learning model. Existing BO algorithms could converge slowly even collapse when the potential observation noise…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

Stochastic Optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. As the latter is often unknown, Distributionally Robust…

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…

A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. Automating the process of choosing the best forecasting model and its corresponding parameters can result to improve a wide…

In real world, our datasets often contain outliers. Moreover, the outliers can seriously affect the final machine learning result. Most existing algorithms for handling outliers take high time complexities (e.g. quadratic or cubic…

We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…

In this article, we present a problem of nonlinear constraint optimization with equality and inequality constraints. Objective functions are defined to be nonlinear and optimizers may have a lower and upper bound. We solve the optimization…

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…