相关论文: An Improved Primal-Dual Interior Point Solver for …

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation…

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…

Due to critical environmental issues, the power systems have to accommodate a significant level of penetration of renewable generation which requires smart approaches to the power grid control. Associated optimal control problems are…

Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…

We study preconditioned proximal point methods for a class of saddle point problems, where the preconditioner decouples the overall proximal point method into an alternating primal--dual method. This is akin to the Chambolle--Pock method or…

The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…

We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual…

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…

In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

Input constrained Model predictive control (MPC) includes an optimization problem which should iteratively be solved at each time-instance. The well-known drawback of model predictive control is the computational cost of the optimization…

We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…

Recently, several authors have suggested the use of first order methods, such as fast dual ascent and the alternating direction method of multipliers, for embedded model predictive control. The main reason is that they can be implemented…

We develop a new inexact interior-point Lagrangian decomposition method to solve a wide range class of constrained composite convex optimization problems. Our method relies on four techniques: Lagrangian dual decomposition, self-concordant…

The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant…

We study a block-structured class of convex-concave saddle-point problems in which both the primal and dual variables admit natural separable decompositions. Motivated by large-scale applications where a full update on either side can be…