Related papers: Generalized Scaling for the Constrained Maximum-En…
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…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods:…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
We consider combinatorial optimization problems defined over random ensembles, and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…