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Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…

Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…

In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train…

Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…

We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…

The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…

This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the…

Ensemble techniques are frequently encountered in machine learning and engineering problems since the method combines different models and produces an optimal predictive solution. The ensemble concept can be adapted to deep learning models…

High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for…

Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh…

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control…

We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type $Y''(x) = f(x,Y(x))$. For numerical illustration, an estimation of the approximation error, an…

We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…

In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…

We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…

Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling. Typically, so called simplified vine copula models are estimated where bivariate conditional copulas are approximated by…