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A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
Discontinuous visibility changes remain a major bottleneck when optimizing surfaces within a physically-based inverse renderer. Many previous works have proposed sophisticated algorithms and data structures to sample visibility silhouettes…
Autonomous agents face the challenge of coordinating multiple tasks (perception, motion planning, controller) which are computationally expensive on a single onboard computer. To utilize the onboard processing capacity optimally, it is…
There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…
The optimization of fuel-optimal low-thrust collision avoidance maneuvers (CAMs) in scenarios involving multiple encounters between spacecraft is addressed. The optimization's objective is the minimization of the total fuel consumption…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind…
This paper presents an extension to the KinectFusion algorithm which allows creating simplified 3D models with high quality RGB textures. This is achieved through (i) creating model textures using images from an HD RGB camera that is…
We introduce an implicit representation of continuous, bijective, orientation-preserving maps between genus zero surfaces with or without boundary. The distortion of these maps can easily be minimized by optimizing the Ginzburg-Landau…
Remarkable advances have been achieved recently in learning neural representations that characterize object geometry, while generating textured objects suitable for downstream applications and 3D rendering remains at an early stage. In…
This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently…
This paper presents a spatial optimization methodology that extends the Spatial Packaging of Interconnected Systems with Physical Interaction (SPI2) framework to support arbitrary, non-convex design boundaries. We introduce a smooth,…