We introduce a new method for a task of maximal material utilization, which is is to fit a flexible, scalable three-dimensional body into another aiming for maximal volume whereas position and shape may vary. The difficulty arises from the containment constraint which is not easy to handle numerically. We use a collision detection method to … Read more
We suggest a new variant of a row layout problem: Find an ordering of n departments with given lengths such that the total weighted sum of their distances to a given checkpoint is minimized. The Checkpoint Ordering Problem (COP) is both of theoretical and practical interest. It has several applications and is conceptually related to … Read more
The $k$-Parallel Row Ordering Problem (kPROP) is an extension of the Single-Row Facility Layout Problem (SRFLP) that considers arrangements of the departments along more than one row. We propose an exact algorithm for the kPROP that extends the semidefinite programming approach for the SRFLP by modelling inter-row distances as products of ordering variables. For k=2 … Read more
This paper describes tight extended formulations for independent set. The first formulation is for arbitrary independence systems and has size $O(n+\mu)$, where $\mu$ denotes the number of inclusion-wise maximal independent sets. Consequently, the extension complexity of the independent set polytope of graphs is $O(1.4423^n)$. The size $O(2^\tw n)$ of the second extended formulation depends on … Read more
We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the … Read more
We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing over a randomly chosen dual variable and minimizing over the primal variable. An … Read more
We study the iterate convergence of strong descent algorithms applied to convex functions. We assume that the function satisfies a very simple growth condition around its minimizers, and then show that the trajectory described by the iterates generated by any such method has finite length, which proves that the sequence of iterates converge. Citation Federal … Read more
\begin{abstract} The existing choices for the step lengths used by the classical steepest descent algorithm for minimizing a convex quadratic function require in the worst case $ \Or(C\log(1/\eps)) $ iterations to achieve a precision $ \eps $, where $ C $ is the Hessian condition number. We show how to construct a sequence of step … Read more
The primal-dual algorithm recently proposed by Chambolle \& Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle \& Pock in \cite{CP11} and also by Shefi \& Teboulle in \cite{ST14} that CPA and variants are closely related to preconditioned versions of the popular alternating direction method of … Read more
We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results. Article Download View On the ergodic convergence rates of a first-order primal-dual algorithm