Related papers: Packing under Convex Quadratic Constraints
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
For any given $\epsilon>0$ we provide an algorithm for the Quadratic Knapsack Problem that has an approximation ratio within $O(n^{2/5+\epsilon})$ and a run time within $O(n^{9/\epsilon})$.
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
We study different online optimization problems in the random-order model. There is a finite set of bins with known capacity and a finite set of items arriving in a random order. Upon arrival of an item, its size and its value for each of…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among…
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…
Location Routing is a fundamental planning problem in logistics, in which strategic location decisions on the placement of facilities (depots, distribution centers, warehouses etc.) are taken based on accurate estimates of operational…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
In this paper, we study the Maximum Profit Pick-up Problem with Time Windows and Capacity Constraint (MP-PPTWC). Our main results are 3 polynomial time algorithms, all having constant approximation factors. The first algorithm has an…
We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…