相关论文: A line search filter sequential adaptive cubic reg…

In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…

Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…

This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the…

In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good…

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…

The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…

This paper studies consensus-based decentralized stochastic optimization for minimizing possibly non-convex expected objectives with convex non-smooth regularizers and nonlinear functional inequality constraints. We reformulate the…

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…

In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other…

We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…

This paper develops a unified high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often exhibit a gap: the function-value residual decreases fast,…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…

Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…