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In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack. Each item has integral width, integral height and an associated integral profit. The goal is…

Data Structures and Algorithms · Computer Science 2021-03-18 Arindam Khan , Arnab Maiti , Amatya Sharma , Andreas Wiese

We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…

Data Structures and Algorithms · Computer Science 2016-10-10 Shi Li

We present a simple and at the same time fficient algorithm to compute all nondominated extreme points in the outcome set of multi-objective mixed integer linear programmes in any dimension. The method generalizes the well-known dichotomic…

Optimization and Control · Mathematics 2019-11-21 Anthony Przybylski , Kathrin Klamroth , Renaud Lacour

Cutting planes are frequently used for solving integer programs. A common strategy is to derive cutting planes from building blocks or a substructure of the integer program. In this paper, we focus on knapsack constraints that arise from…

Optimization and Control · Mathematics 2025-08-19 Christopher Hojny , Cédric Roy

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

Optimization and Control · Mathematics 2018-12-19 Areesh Mittal , Can Gokalp , Grani A. Hanasusanto

An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…

Data Structures and Algorithms · Computer Science 2024-03-04 Moritz Buchem , Paul Deuker , Andreas Wiese

This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…

Optimization and Control · Mathematics 2018-01-11 Shana Moothedath , Prasanna Chaporkar , Madhu N. Belur

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…

Data Structures and Algorithms · Computer Science 2020-09-16 Yuri Faenza , Danny Segev , Lingyi Zhang

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program,…

Optimization and Control · Mathematics 2022-08-31 Ankur Sinha , Arka Das , Guneshwar Anand , Sachin Jayaswal

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…

Data Structures and Algorithms · Computer Science 2024-11-26 Antonios Antoniadis , Marek Eliáš , Adam Polak , Moritz Venzin

In the \textsc{2-Dimensional Knapsack} problem (2DK) we are given a square knapsack and a collection of $n$ rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed…

Computational Geometry · Computer Science 2021-03-19 Waldo Gálvez , Fabrizio Grandoni , Arindam Khan , Diego Ramírez-Romero , Andreas Wiese

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

Data Structures and Algorithms · Computer Science 2009-09-29 Christoph Durr , Mathilde Hurand

We study the three-dimensional Knapsack (3DK) problem, in which we are given a set of axis-aligned cuboids with associated profits and an axis-aligned cube knapsack. The objective is to find a non-overlapping axis-aligned packing (by…

Data Structures and Algorithms · Computer Science 2025-03-26 Klaus Jansen , Debajyoti Kar , Arindam Khan , K. V. N. Sreenivas , Malte Tutas

We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…

Data Structures and Algorithms · Computer Science 2021-02-12 Arindam Khan , Eklavya Sharma , K. V. N. Sreenivas

Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…

Optimization and Control · Mathematics 2025-01-22 Levin Nemesch , Stefan Ruzika , Clemens Thielen , Alina Wittmann

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…

Optimization and Control · Mathematics 2016-11-04 Sven Mallach

The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…

Optimization and Control · Mathematics 2019-07-05 Grigori German , Hadrien Cambazard , Jean-Philippe Gayon , Bernard Penz

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

Optimization and Control · Mathematics 2026-02-19 Welington de Oliveira , Johannes O. Royset

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Numerical Analysis · Computer Science 2017-02-15 Roberto Mínguez , Víctor Casero-Alonso