Related papers: On "A Homogeneous Interior-Point Algorithm for Non…
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 propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…
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…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
Dual first-order methods are essential techniques for large-scale constrained convex optimization. However, when recovering the primal solutions, we need $T(\epsilon^{-2})$ iterations to achieve an $\epsilon$-optimal primal solution when we…
We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…
This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…
The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [16,19] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few…
Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…
He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in…
Many problems in statistical learning, imaging, and computer vision involve the optimization of a non-convex objective function with singularities at the boundary of the feasible set. For such challenging instances, we develop a new…
This paper explores a surprising equivalence between two seemingly-distinct convex optimization methods. We show that simulated annealing, a well-studied random walk algorithms, is directly equivalent, in a certain sense, to the central…
We present a head-to-head evaluation of the Improved Inexact--Newton--Smart (INS) algorithm against a primal--dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method…
Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…