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The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational…
We study stochastic combinatorial optimization problems where the objective is to minimize the expected maximum load (a.k.a.\ the makespan). In this framework, we have a set of $n$ tasks and $m$ resources, where each task $j$ uses some…
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample…
In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m x 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection…
The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion…
The problem of the mean-square optimal linear estimation of the functional $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values of stochastic stationary process $\xi(t)$ from observations of the process…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
In the context of Noisy Multi-Objective Optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used to evaluate the…
We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound…
High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…