Related papers: A New Approach for Finding the Global Optimal Poin…
In robotic task planning, symbolic planners using rule-based representations like PDDL are effective but struggle with long-sequential tasks in complicated environments due to exponentially increasing search space. Meanwhile, LLM-based…
We propose a method for verifying that a given feasible point for a polynomial optimization problem is globally optimal. The approach relies on the Lasserre hierarchy and the result of Lasserre regarding the importance of the convexity of…
Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…
We propose a novel iterative method for optimally placing and orienting multiple cameras in a 3D scene. Sample applications include improving the accuracy of 3D reconstruction, maximizing the covered area for surveillance, or improving the…
Simultaneous localization and mapping (SLAM) has been a hot research field in the past years. Against the backdrop of more affordable 3D LiDAR sensors, research on 3D LiDAR SLAM is becoming increasingly popular. Furthermore, the…
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…
In this paper, a new sequential surrogate-based optimization (SSBO) algorithm is developed, which aims to improve the global search ability and local search efficiency for the global optimization of expensive black-box models. The proposed…
In this article we provide an experimental algorithm that in many cases gives us an upper bound of the global infimum of a real polynomial on $\R^{n}$. It is very well known that to find the global infimum of a real polynomial on $\R^{n}$,…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Answering exact shortest path distance queries is a fundamental task in graph theory. Despite a tremendous amount of research on the subject, there is still no satisfactory solution that can scale to billion-scale complex networks.…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Globally localizing in a given map is a crucial ability for robots to perform a wide range of autonomous navigation tasks. This paper presents OneShot - a global localization algorithm that uses only a single 3D LiDAR scan at a time, while…
The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an…
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing…
We study the problem of unsupervised 3D semantic segmentation on raw point clouds without needing human labels in training. Existing methods usually formulate this problem into learning per-point local features followed by a simple grouping…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
This paper presents a hierarchical segment-based optimization method for Simultaneous Localization and Mapping (SLAM) system. First we propose a reliable trajectory segmentation method that can be used to increase efficiency in the back-end…
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…