Related papers: A Proximal Augmented Lagrangian Method Based on Qu…
We consider the estimation of the state transition matrix in vector autoregressive models, when time sequence data is limited but nonsequence steady-state data is abundant. To leverage both sources of data, we formulate the least squares…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve…
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…
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…
In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In this paper we propose a splitting scheme which hybridizes generalized conditional gradient with a proximal step which we call CGALP algorithm, for minimizing the sum of three proper convex and lower-semicontinuous functions in real…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
The proximal alternating linearized minimization method (PALM) suits well for solving block-structured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g.,…
Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…