Worst-Case Analysis of Heuristic Approaches for the Temporal Bin Packing Problem with Fire-Ups

We consider the temporal bin packing problem with fire-ups (TBPP-FU), a branch of operations research recently introduced in multi-objective cloud computing. In this scenario, any item is equipped with a resource demand and a lifespan meaning that it requires the bin capacity only during that time interval. We then aim at finding a schedule minimizing … Read more

A MILP Approach to DRAM Access Worst-Case Analysis

The Dynamic Random Access Memory (DRAM) is among the major points of contention in multi-core systems. We consider a challenging optimization problem arising in worst-case performance analysis of systems architectures: computing the worst-case delay (WCD) experienced when accessing the DRAM due to the interference of contending requests. The WCD is a crucial input for micro-architectural … Read more

Analysis of Process Flexibility Designs under Disruptions

Most of the previous studies of process flexibility designs have focused on expected sales and demand uncertainty. In this paper, we examine the worst-case performance of flexibility designs in the case of demand and supply uncertainties, where the latter can be in the form of either plant or arc disruptions. We define the Plant Cover … Read more

Universal regularization methods – varying the power, the smoothness and the accuracy

Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of adaptive regularization methods, that use first- or higher-order local Taylor models of the objective regularized by a(ny) power of the step size and applied … Read more

The Stochastic Multistage Fixed Charge Transportation Problem: Worst-Case Analysis of the Rolling Horizon Approach

We introduce the Stochastic multistage ﬁxed charge transportation problem in which a producer has to ship an uncertain load to a customer within a deadline. At each time period, a ﬁxed transportation price can be paid to buy a transportation capacity. If the transportation capacity is used, the supplier also pays an uncertain unit transportation … Read more

Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of $O(\epsilon^{-3/2})$ proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an $\epsilon$-approximate first-order critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where high-order derivatives are … Read more

Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models

The evaluation complexity of general nonlinear, possibly nonconvex,constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem’s function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, … Read more

Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization

In a recent paper (Cartis, Gould and Toint, Math. Prog. A 144(1-2) 93–106, 2014), the evaluation complexity of an algorithm to find an approximate first-order critical point for the general smooth constrained optimization problem was examined. Unfortunately, the proof of Lemma 3.5 in that paper uses a result from an earlier paper in an incorrect … Read more

On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization

We propose a new termination criteria suitable for potentially singular, zero or non-zero residual, least-squares problems, with which cubic regularization variants take at most $\mathcal{O}(\epsilon^{-3/2})$ residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below $\epsilon$; this is the best-known bound for potentially singular nonlinear least-squares problems. We then … Read more

A Note About The Complexity Of Minimizing Nesterov’s Smooth Chebyshev-Rosenbrock Function

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre (2011) implying a very large lower bound on the number of iterations required to reach the solution’s neighbourhood for a specific problem with … Read more