Related papers: Scalable Co-Design via Linear Design Problems: Com…
One of the challenges of modern engineering, and robotics in particular, is designing complex systems, composed of many subsystems, rigorously and with optimality guarantees. This paper introduces a theory of co-design that describes…
An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the…
Complex engineered systems require coordinated design choices across heterogeneous components under multiple conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems by…
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…
Hierarchical architectures are critical to the scalability of reinforcement learning methods. Current hierarchical frameworks execute actions serially, with macro-actions comprising sequences of primitive actions. We propose a novel…
Many problems in robotics require reasoning over a mix of continuous dynamics and discrete events, such as making and breaking contact in manipulation and locomotion. These problems are locally well modeled by linear complementarity…
This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Markov Decision Processes (MDPs) are stochastic optimization problems that model situations where a decision maker controls a system based on its state. Partially observed Markov decision processes (POMDPs) are generalizations of MDPs where…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Many engineered systems must balance competing objectives, such as performance and safety, cost and reliability, or efficiency and sustainability, and are naturally modeled as compositions of interacting subsystems. We study online…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite…
We focus on designing combinatorial algorithms for the Capacitated Network Design problem (Cap-SNDP). The Cap-SNDP is the problem of satisfying connectivity requirements when edges have costs and hard capacities. We begin by showing that…