Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints

• URL: http://arxiv.org/abs/2201.07657v3
• Date: Sat, 2 Dec 2023 20:11:53 GMT
• Title: Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints
• Authors: Le Thi Khanh Hien, Dimitri Papadimitriou
• Abstract summary: We propose a method of multipliers for solving a class of multiblock nonsmooth alternating optimization problem with nonlinear constraints. We employ a major sequenceization procedure in update of each block of the primal variables.
• Score: 3.2815423235774634
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in the update of each block of the primal variables. Subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian are proved. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.

Related papers

• An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization [2.323238724742687]
  We propose an accelerated block proximal linear framework with adaptive momentum (ABPL$+$) for nonsmooth and nonsmooth optimization. We analyze the potential causes of the extrapolation step failing in some algorithms, and resolve this issue by enhancing the comparison process. We extend our algorithm to any scenario involving updating the gradient step and the linear extrapolation step.
  arXiv  Detail & Related papers  (2023-08-23T13:32:31Z)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• Convex mixed-integer optimization with Frank-Wolfe methods [20.37026309402396]
  Mixed-integer nonlinear optimization presents both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations.
  arXiv  Detail & Related papers  (2022-08-23T14:46:54Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming [17.9230793188835]
  We study nonlinear optimization problems with objective and deterministic equality and inequality constraints. We propose an active-set sequentialAdaptive programming algorithm, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the parameters of augmented Lagrangian and performs line search to decide the stepsize.
  arXiv  Detail & Related papers  (2021-09-23T17:12:17Z)
• Nonlinear matrix recovery using optimization on the Grassmann manifold [18.655422834567577]
  We investigate the problem of recovering a partially observed high-rank clustering matrix whose columns obey a nonlinear structure such as a union of subspaces. We show that the alternating limit converges to a unique point using the Kurdyka-Lojasi property.
  arXiv  Detail & Related papers  (2021-09-13T16:13:13Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems [99.59934203759754]
  We introduce a class of first-order methods for smooth constrained optimization. Two distinctive features of our approach are that projections or optimizations over the entire feasible set are avoided. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear.
  arXiv  Detail & Related papers  (2021-07-17T11:45:13Z)
• A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization [17.553531291690025]
  We propose an algorithmic framework dubbed alternating methods of multipliers (iADMM) for solving a class of non nonsmooth multiblock composite problems. Our framework employs the general-major surrogateization (MM) principle to update each block of variables to unify the convergence analysis of previous ADMM schemes.
  arXiv  Detail & Related papers  (2021-02-10T13:55:28Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.