相关论文: An algebraic geometry approach to nonlinear parame…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines an evolution equation so that in the asymptotic limit a…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…
This expository paper reviews some of the recent uses of computational algebraic geometry in classical and quantum optimization. The paper assumes an elementary background in algebraic geometry and adiabatic quantum computing (AQC), and…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…
This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…