Related papers: New artificial-free phase 1 simplex method
We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…
We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better…
The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
In this chapter we derive computational complexity certifications of first order inexact dual methods for solving general smooth constrained convex problems which can arise in real-time applications, such as model predictive control. When…
This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…
An elementary, but fundamental, operation in disjunctive programming is a basic step, which is the intersection of two disjunctions to form a new disjunction. Basic steps bring a disjunctive set in regular form closer to its disjunctive…
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…
We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into…
One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when…
This paper shows how the variational Bayes method provides a computational efficient technique in the context of hierarchical modelling using Dirichlet process priors, in particular without requiring conjugate prior assumption. It shows,…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
The primal-dual hybrid gradient method (PDHG) is useful for optimization problems that commonly appear in image reconstruction. A downside of PDHG is that there are typically three user-set parameters and performance of the algorithm is…
The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using…
In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…