Related papers: Disciplined Geodesically Convex Programming
Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
Recent methods for learning a linear subspace from data corrupted by outliers are based on convex $\ell_1$ and nuclear norm optimization and require the dimension of the subspace and the number of outliers to be sufficiently small. In sharp…
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…
We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…
We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
This work introduces ShapeGen3DCP, a deep learning framework for fast and accurate prediction of filament cross-sectional geometry in 3D Concrete Printing (3DCP). The method is based on a neural network architecture that takes as input both…
We consider convex-concave saddle point problems, and more generally convex optimization problems we refer to as $\textit{saddle problems}$, which include the partial supremum or infimum of convex-concave saddle functions. Saddle problems…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…
Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
Generalized Polynomial Chaos (gPC) theory has been widely used for representing parametric uncertainty in a system, thanks to its ability to propagate uncertainty evolution. In an optimal control context, gPC can be combined with several…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…