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We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal…
The Procrustes matching (PM) problem is the problem of finding the optimal rigid motion and labeling of two point sets so that they are as close as possible. Both rigid and non-rigid shape matching problems can be formulated as PM problems.…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
In the Directed Latency problem, we are given an asymmetric metric on a set of vertices (or clients), and a given depot $s$. We seek a path $P$ starting at $s$ and visiting all the clients so as to minimize the sum of client waiting times…
Spatial misalignment caused by variations in poses and viewpoints is one of the most critical issues that hinders the performance improvement in existing person re-identification (Re-ID) algorithms. To address this problem, in this paper,…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the…
This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). The problem is formulated as a bi-objective Pareto…
This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of…
In Reinforcement Learning (RL), tasks with instantaneous hard constraints present significant challenges, particularly when the decision space is non-convex or non-star-convex. This issue is especially relevant in domains like autonomous…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
Contact-based motion planning for manipulation, object exploration or balancing often requires finding sequences of fixed and sliding contacts and planning the transition from one contact in the environment to another. However, most…
Viewpoint missing of objects is common in scene reconstruction, as camera paths typically prioritize capturing the overall scene structure rather than individual objects. This makes it highly challenging to achieve high-fidelity…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…
Communication is a major bottleneck in distributed learning, especially in large-scale settings and in federated learning environments with slow links. Three standard ways to reduce this cost are communication compression, local training,…