We study non-parametric estimation of choice models, which was introduced to alleviate unreasonable assumptions in traditional parametric models, and are prevalent in several application areas. Existing literature focuses only on the static observational setting where all of the observations are given upfront, and lacks algorithms that provide explicit convergence rate guarantees or an a priori … Read more
We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using the Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem … Read more
In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments … Read more
This paper presents novel convergence results for the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) in the context of distributed convex optimization. It is shown that ALADIN converges for a large class of convex optimization problems from any starting point to minimizers without needing line-search or other globalization routines. Under additional regularity assumptions, … Read more
We first point out several flaws in the recent paper {\it [R. Shefi, M. Teboulle: Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization, SIAM J. Optim. 24, 269–297, 2014]} that proposes two ADMM-type algorithms for solving convex optimization problems involving compositions with linear operators and show … Read more
In this paper, we propose a new primal-dual algorithm for minimizing f(x)+g(x)+h(Ax), where f, g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. It has some famous primal-dual algorithms for minimizing the sum of two functions as special cases. For example, it reduces … Read more
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for … Read more
In this paper, we focus our study on the convergence of (proximal) gradient methods and accelerated (proximal) gradient methods for smooth (composite) optimization under a H\”{o}lderian error bound (HEB) condition. We first show that proximal gradient (PG) method is automatically adaptive to HEB while accelerated proximal gradient (APG) method can be adaptive to HEB by … Read more
Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in $(0,(1+\sqrt{5})/2)$ have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to $(1+\sqrt{5})/2$. … Read more
The extended second order cones were introduced by S. Z. Németh and G. Zhang in [S. Z. Németh and G. Zhang. Extended Lorentz cones and variational inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for solving mixed complementarity problems and variational inequalities on cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended … Read more