Related papers: New Formulation of Mixed-Integer Conic Programming…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
In this work, we introduce and study the $p$-$\alpha$-closest-center problem ($p\alpha$CCP), which generalizes the $p$-second-center problem, a recently emerged variant of the classical $p$-center problem. In the $p\alpha$CCP, we are given…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that…
This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process, and develops an efficient search algorithm that is able to solve practical instances of the MIP…
One goal of dexterous robotic grasping is to allow robots to handle objects with the same level of flexibility and adaptability as humans. However, it remains a challenging task to generate an optimal grasping strategy for dexterous hands,…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
The maximal biclique enumeration problem in bipartite graphs is fundamental and has numerous applications in E-commerce and transaction networks. Most existing studies adopt a branch-and-bound framework, which recursively expands a partial…
Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in…
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
Recent progress in contact-rich robotic manipulation has been striking, yet most deployed systems remain confined to simple, scripted routines. One of the key barriers is the lack of motion planning algorithms that can provide verifiable…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…
Grasp planning is an important task for robotic manipulation. Though it is a richly studied area, a standalone, fast, and differentiable grasp planner that can work with robot grippers of different DOFs has not been reported. In this work,…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
Grasping is fundamental to robotic manipulation, and recent advances in large-scale grasping datasets have provided essential training data and evaluation benchmarks, accelerating the development of learning-based methods for robust object…
We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…
We propose a mixed-integer linear program (MILP) for multi-agent motion planning that embeds Polytopic Action-based Motion Planning (PAAMP) into a sequence-then-solve pipeline. Region sequences confine each agent to adjacent convex…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…