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Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in…
Stochastic programming models can lead to very large-scale optimization problems for which it may be impossible to enumerate all possible scenarios. In such cases, one adopts a sampling-based solution methodology in which case the…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
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…
During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as…
This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while…
Sampling-based planning is the predominant paradigm for motion planning in robotics. Most sampling-based planners use a global random sampling scheme to guarantee probabilistic completeness. However, most schemes are often inefficient as…
Current methods for end-to-end constructive neural combinatorial optimization usually train a policy using behavior cloning from expert solutions or policy gradient methods from reinforcement learning. While behavior cloning is…
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…
We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
In this paper, we present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…