Related papers: Scalable Co-Design via Linear Design Problems: Com…
We present a versatile framework for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are typically based on random sampling or concurrent optimization. We propose a novel bilevel…
We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
Practically all of the planning research is limited to states represented in terms of Boolean and numeric state variables. Many practical problems, for example, planning inside complex software systems, require far more complex data types,…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
When designing autonomous systems, we need to consider multiple trade-offs at various abstraction levels, and the choices of single (hardware and software) components need to be studied jointly. In this work we consider the problem of…
Space mission planning and spacecraft design are tightly coupled and need to be considered together for optimal performance; however, this integrated optimization problem results in a large-scale Mixed-Integer Nonlinear Programming (MINLP)…
Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming…
Large language models (LLMs) have emerged as powerful tools for many AI problems and exhibit remarkable in-context learning (ICL) capabilities. Compositional ability, solving unseen complex tasks that combine two or more simple tasks, is an…
In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems,…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Large language models (LLMs) are often constrained by rigid reasoning processes, limiting their ability to generate creative and diverse responses. To address this, a novel framework called LADDER is proposed, combining Chain-of-Thought…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…
The growing need to integrate information from a large number of diverse sources poses significant scalability challenges for data integration systems. These systems often rely on manually written schema mappings, which are complex,…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Multiple patterning lithography has been widely adopted in advanced technology nodes of VLSI manufacturing. As a key step in the design flow, multiple patterning layout decomposition (MPLD) is critical to design closure. Due to the…