相关论文: Lagrangian Relaxation for MAP Estimation in Graphi…

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient…

Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state…

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…

In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…

The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…

We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…

We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…

We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous…

Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…

This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…

Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…

We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…

This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach…