Related papers: A primal-dual interior-point method capable of rap…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. We assume that the learner is not allowed to interact with the expert…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…
We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by constructing a family of linear programs with $3r+1$ inequalities in dimension $2r$ for which the number of iterations performed is in…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…
We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive…
This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can…
Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as NSDPs. As far as we know, the current algorithms for NSDPs only…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…