Related papers: Polynomial Optimization via Random Projection and …

Black-box optimization is a powerful approach for discovering global optima in noisy and expensive black-box functions, a problem widely encountered in real-world scenarios. Recently, there has been a growing interest in leveraging domain…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and…

Many planning applications involve complex relationships defined on high-dimensional, continuous variables. For example, robotic manipulation requires planning with kinematic, collision, visibility, and motion constraints involving robot…

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…

We study a class of projective transformations of spectraplexes associated with self-dual cones and, on this basis, propose a polynomial-time algorithm for convex feasibility problems with positive definite constraints. At each iteration of…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…

The floating-point implementation of a function on an interval often reduces to polynomial approximation, the polynomial being typically provided by Remez algorithm. However, the floating-point evaluation of a Remez polynomial sometimes…

This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models.…

We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…

One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by…

Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…

Black-box and preference-based optimization algorithms are global optimization procedures that aim to find the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons…

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…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…