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This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
The minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality.…
In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…
This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
The proximal point algorithm plays a central role in non-smooth convex programming. The Augmented Lagrangian Method, one of the most famous optimization algorithms, has been found to be closely related to the proximal point algorithm. Due…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation,…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
Sampling-based optimization (SBO), like cross-entropy method and evolutionary algorithms, has achieved many successes in solving non-convex problems without gradients, yet its convergence is poorly understood. In this paper, we establish a…
We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the…
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…