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We show NP-hardness of a generalized quadratic programming problem, which we called Unconstrained N-ary Quadratic Programming (UNQP). This problem has recently become practically relevant in the context of novel memristor-based neuromorphic…
We study matrix estimation problems arising in reinforcement learning (RL) with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it…
Integer programming (IP) has proven to be highly effective in solving many path-based optimization problems in robotics. However, the applications of IP are generally done in an ad-hoc, problem specific manner. In this work, after examined…
Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
Visual Place Recognition (VPR) is a critical task for performing global re-localization in visual perception systems. It requires the ability to accurately recognize a previously visited location under variations such as illumination,…
This paper presents a unified framework that connects sequential quadratic programming (SQP) and the iterative linear-parameter-varying model predictive control (LPV-MPC) technique. Using the differential formulation of the LPV-MPC, we…
As quantum computing technology advances, the complexity of quantum algorithms increases, necessitating a shift from low-level circuit descriptions to high-level programming paradigms. This paper addresses the challenges of developing a…
Low-rank architectures have become increasingly important for efficient large language model (LLM) pre-training, providing substantial reductions in both parameter complexity and memory/computational demands. Despite these advantages,…
This paper introduces the quadratically-constrained quadratic programming (QCQP) framework recently added in HPIPM alongside the original quadratic-programming (QP) framework. The aim of the new framework is unchanged, namely providing the…
The extensive memory footprint of language model (LM) fine-tuning poses a challenge for both researchers and practitioners. LMs use an embedding matrix to represent extensive vocabularies, forming a substantial proportion of the model…
The low rank MDP has emerged as an important model for studying representation learning and exploration in reinforcement learning. With a known representation, several model-free exploration strategies exist. In contrast, all algorithms for…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum…
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…