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In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
A composite quadric model (CQM) is an object modeled by piecewise linear or quadric patches. We study the continuous detection problem of a special type of CQM objects which are commonly used in CAD/CAM, that is, the boundary surfaces of…
Estimating collision probabilities between robots and environmental obstacles or other moving agents is crucial to ensure safety during path planning. This is an important building block of modern planning algorithms in many application…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Collision detection is a core component of robotics applications such as simulation, control, and planning. Traditional algorithms like GJK+EPA compute witness points (i.e., the closest or deepest-penetration pairs between two objects) but…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
We present a computational methodology for obtaining rotationally symmetric sets of points satisfying discrete geometric constraints, and demonstrate its applicability by discovering new solutions to some well-known problems in…
The Lucas & Kanade (LK) algorithm is the method of choice for efficient dense image and object alignment. The approach is efficient as it attempts to model the connection between appearance and geometric displacement through a linear…
A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of…
Monocular depth estimation (MDE) plays a pivotal role in various computer vision applications, such as robotics, augmented reality, and autonomous driving. Despite recent advancements, existing methods often fail to meet key requirements…
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…
We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is…
We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find…
Control co-design (CCD) is a technique for improving the closed-loop performance of systems through the coordinated design of both plant parameters and an optimal control policy. While model predictive control (MPC) is an attractive control…
Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…
We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane…
We study joint optimization of service placement, request routing, and CPU sizing in a cooperative MEC system. The problem is considered from the perspective of the service provider (SP), which delivers heterogeneous MEC-enabled…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such…