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Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
Primal heuristics play a crucial role in quickly finding feasible solutions for NP-hard integer linear programming (ILP). Although $\textit{end-to-end learning}$-based primal heuristics (E2EPH) have recently been proposed, they are…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…