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Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…

Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…

Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…

Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that…

We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type…

Under the assumption of (positive) homogeneity (PH in the sequel) of the corresponding utility functions, we construct polynomial time algorithms for the weak separability, the collective consumption behavior and some related problems.…

In this article, we introduce the interval optimization problems (IOPs) on Hadamard manifolds as well as study the relationship between them and the interval variational inequalities. To achieve the theoretical results, we build up some new…

A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…

We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…

This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and operations grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by the combination…

Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…

We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or job has an arrival time, a deadline, a length and a weight. The objective is to maximize the total weight of completed intervals or jobs.…

We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the…

This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…

We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First,…

The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…

Subset selection is an interesting and important topic in the field of evolutionary multi-objective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive, subset selection is an essential post-processing…