Related papers: Global optimization for low-dimensional switching …
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
In this paper, we develop a new concept of Global Curvature Bound for an arbitrary nonlinear operator between abstract metric spaces. We use this notion to characterize the global complexity of high-order algorithms solving composite…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the…
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…
We address rotation averaging (RA) and its application to real-world 3D reconstruction. Local optimisation based approaches are the de facto choice, though they only guarantee a local optimum. Global optimisers ensure global optimality in…
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…