Related papers: A Dual Ascent Framework for Lagrangean Decompositi…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The…
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…