A New Algebraic Geometry Algorithm for Integer Programming

TL;DR: An algebraic approach is proposed to maximize the expected return under a given admissible level of risk measured by the covariance matrix to reach an optimal portfolio.

TL;DR: This work proposes a novel hybrid quantum-classical approach to calculate Graver bases, which have the potential to solve a variety of hard linear and non-linear integer programs, as they form a test set (optimality certificate) with very appealing properties.

TL;DR: Some centralised production-inventory models that have been of service to contemporary business practices in decentralised decision-making settings are discussed in this paper, where the authors focus on the parallel and connected development of academic models for managing inventories and their actual applications in industry.

TL;DR: This paper provides the first general purpose computational procedure that can be used directly as a $translator$ to solve polynomial integer optimization to solve AQC problems.

TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.

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Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

TL;DR: In the Groebner package, the most commonly used commands are NormalForm, for doing the division algorithm, and Basis, for computing a Groebners basis as mentioned in this paper. But these commands require a large number of variables.