Related papers: Bundle methods for dual atomic pursuit
One common approach for dose optimization is a two-stage design, which initially conducts dose escalation to identify the maximum tolerated dose (MTD), followed by a randomization stage where patients are assigned to two or more doses to…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
Topology optimisation of trusses can be formulated as a combinatorial and multi-modal problem in which locating distinct optimal designs allows practitioners to choose the best design based on their preferences. Bilevel optimisation has…
In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…
Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to…
The domain of online algorithms with predictions has been extensively studied for different applications such as scheduling, caching (paging), clustering, ski rental, etc. Recently, Bamas et al., aiming for an unified method, have provided…
The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…
Distributed optimization provides a framework for deriving distributed algorithms for a variety of multi-robot problems. This tutorial constitutes the first part of a two-part series on distributed optimization applied to multi-robot…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving optimization problems with nonsmooth components. In this paper, we conduct a theoretical investigation of a modified proximal bundle…
Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
We provide an overview of primal-dual algorithms for nonsmooth and non-convex-concave saddle-point problems. This flows around a new analysis of such methods, using Bregman divergences to formulate simplified conditions for convergence.
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
The weighted sum method is a simple and widely used technique that scalarizes multiple conflicting objectives into a single objective function. It suffers from the problem of determining the appropriate weights corresponding to the…