相关论文: A Gilmore-Gomory-Type Construction of Integer Prog…
The existing software requirement selection methods have mainly focused on optimizing the economic value of a software product while ignoring its social values and their long-term impacts on the society. Social values however, are also…
Configuration integer programs (IP) have been key in the design of algorithms for NP-hard high-multiplicity problems since the pioneering work of Gilmore and Gomory [Oper. Res., 1961]. Configuration IPs have a variable for each possible…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to…
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
Recently discovered polyhedral structures of the value function for finite state-action discounted Markov decision processes (MDP) shed light on understanding the success of reinforcement learning. We investigate the value function polytope…
We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered…
We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits,…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
A novel matching based heuristic algorithm designed to detect specially formulated infeasible zero-one IPs is presented. The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…
Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…
In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law…
In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter…
Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this…
We consider the problem of selecting a portfolio of entries of fixed cardinality for contests with top-heavy payoff structures, i.e. most of the winnings go to the top-ranked entries. This framework is general and can be used to model a…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…