Related papers: Pose Graph Optimization in the Complex Domain: Lag…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
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…
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…
Graph matching aims to find correspondences between two graphs. This paper integrates several well-known graph matching algorithms into a framework: the constrained gradient method. The primary difference among these algorithms lies in…
The ubiquity of massive graph data sets in numerous applications requires fast algorithms for extracting knowledge from these data. We are motivated here by three electrical measures for the analysis of large small-world graphs $G = (V, E)$…
We propose a new splitting and successively solving augmented Lagrangian (SSAL) method for solving an optimization problem with both semicontinuous variables and a cardinality constraint. This optimization problem arises in several contexts…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
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 investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the…
In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
The $\ell_p$ regularization problem with $0< p< 1$ has been widely studied for finding sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. The proximal gradient…
Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to…
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…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…
Seeking the external equitable partitions (EEPs) of networks under unknown structures is an emerging problem in network analysis. The special structure of EEPs has found widespread applications in many fields such as cluster synchronization…