Related papers: Constrained consensus-based optimization
This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and,…
Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones,…
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
In this paper, we introduce a novel variant of the CBO method that incorporates jumps according to an $\alpha$-stable stochastic process in a kinetic framework. This extension gives rise to nonlocal stochastic effects, which improve the…
In this chapter we give an overview of the consensus-based global optimization algorithm and its recent variants. We recall the formulation and analytical results of the original model, then we discuss variants using component-wise…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter $\kappa \in (0,1)$. Under minimal assumptions on the objective function and the initial data, we establish its…
Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal…
Bayesian optimization (BO) is a popular method for optimizing expensive-to-evaluate black-box functions. BO budgets are typically given in iterations, which implicitly assumes each evaluation has the same cost. In fact, in many BO…
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we…
In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…
Population-based methods can cope with a variety of different problems, including problems of remarkably higher complexity than those traditional methods can handle. The main procedure consists of successively updating a population of…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and…