相关论文: A Gilmore-Gomory-Type Construction of Integer Prog…

Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…

We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is…

The winner determination problems of many attractive multi-winner voting rules are NP-complete. However, they often admit polynomial-time algorithms when restricting inputs to be single-peaked. Commonly, such algorithms employ dynamic…

Integer programming (IP) is a general optimization framework widely applicable to a variety of unstructured and structured problems arising in, e.g., scheduling, production planning, and graph optimization. As IP models many provably hard…

We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of…

We consider a fundamental integer programming (IP) model for cost-benefit analysis flood protection through dike building in the Netherlands, due to Verweij and Zwaneveld. Experimental analysis with data for the Ijsselmeer lead to integral…

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…

Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…

Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…

We describe a nonlinear generalization of dual dynamic programming theory and its application to value function estimation for deterministic control problems over continuous state and action spaces, in a discrete-time infinite horizon…

Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…

We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. We create…

In this work, an integer linear programming (ILP) based model is proposed for the computation of a minimal cost addition sequence for a given set of integers. Since exponents are additive under multiplication, the minimal length addition…

We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…

We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…

Chvatal-Gomory cutting planes (CG-cuts for short) are a fundamental tool in Integer Programming. Given any single CG-cut, one can derive an entire family of CG-cuts, by `iterating' its multiplier vector modulo one. This leads naturally to…

We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…

Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…

Many sequential decision making problems can be formulated as an adaptive submodular maximization problem. However, most of existing studies in this field focus on pool-based setting, where one can pick items in any order, and there have…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…