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

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such…

In the application of the Expectation Maximization algorithm to identification of dynamical systems, internal states are typically chosen as latent variables, for simplicity. In this work, we propose a different choice of latent variables,…

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…

A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

"Weakly coupled dynamic program" describes a broad class of stochastic optimization problems in which multiple controlled stochastic processes evolve independently but subject to a set of linking constraints imposed on the controls. One…

We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

Given a graph $G=(V,E)$ and a set $C$ of unordered pairs of edges regarded as being in conflict, a stable spanning tree in $G$ is a set of edges $T$ inducing a spanning tree in $G$, such that for each $\left\lbrace e_i, e_j \right\rbrace…

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we…

In this paper, we aim at unifying, simplifying and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem.…

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…

We propose a scalable approximate algorithm for the NP-hard maximum-weight independent set problem. The core component of our algorithm is a dual coordinate descent applied to a smoothed LP relaxation of the problem. This technique is…

We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and $\ell^p$ regression. In each iteration, the scheme solves only a weighted least-squares…

We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…