Related papers: An Augmented Lagrangian Method for Optimization Pr…
The leaky ReLU network with a group sparse regularization term has been widely used in the recent years. However, training such a network yields a nonsmooth nonconvex optimization problem and there exists a lack of approaches to compute a…
We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…
This study investigates imposing hard inequality constraints on the outputs of convolutional neural networks (CNN) during training. Several recent works showed that the theoretical and practical advantages of Lagrangian optimization over…
The augmented Lagrange method is employed to address the optimal control problem involving pointwise state constraints in parabolic equations. The strong convergence of the primal variables and the weak convergence of the dual variables are…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
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…
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…
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…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on…
In this work we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which…
In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…
This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the…
This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving smooth nonconvex composite optimization problems with nonlinear $\cal K$-convex constraints, i.e., the constraints are convex with respect to…