Related papers: Active Set Algorithm for Large-Scale Continuous Kn…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
We study a robust extensible bin packing problem with budgeted uncertainty, under a budgeted uncertainty model where item sizes are defined to lie in the intersection of a box with a one-norm ball. We propose a scenario generation algorithm…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…
In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero…
Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, many applications require exact solutions, as approximate…
Constrained optimization underlies crucial societal problems (for instance, stock trading and bandwidth allocation), but is often computationally hard (complexity grows exponentially with problem size). The big-data era urgently demands…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
In stochastic combinatorial optimization, algorithms differ in their adaptivity: whether or not they query realized randomness and adapt to it. Dean et al. (FOCS '04) formalize the adaptivity gap, which compares the performance of fully…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
Optimizing objective functions stands to benefit significantly from leveraging quantum computers, promising enhanced solution quality across various application domains in the future. However, harnessing the potential of quantum solvers…
This paper presents active-set methods for minimizing nonconvex twice-continuously differentiable functions subject to bound constraints. Within the faces of the feasible set, we employ descent methods with Armijo line search, utilizing…