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Agentic AI systems are emerging as powerful tools for automating complex, multi-step tasks across various industries. One such industry is telecommunications, where the growing complexity of next-generation radio access networks (RANs)…

Large Language Models (LLMs) have revolutionized Natural Language Processing but exhibit limitations, particularly in autonomously addressing novel challenges such as reasoning and problem-solving. Traditional techniques like…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly…

We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…

Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…

Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…

The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike…

The actor-critic (AC) reinforcement learning algorithms have been the powerhouse behind many challenging applications. Nevertheless, its convergence is fragile in general. To study its instability, existing works mostly consider the…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

Large Language Model (LLM)-based autonomous agents are expected to play a vital role in the evolution of 6G networks, by empowering real-time decision-making related to management and service provisioning to end-users. This shift…

Many reinforcement learning methods achieve great success in practice but lack theoretical foundation. In this paper, we study the convergence analysis on the problem of the Linear Quadratic Regulator (LQR). The global linear convergence…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Given a network of agents, we study the problem of designing a distributed algorithm that computes k independent weighted means of the network's initial conditions (namely, the agents agree on a k-dimensional space). Akin to average…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional…

We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently…