Journal ArticleDOI
There Cannot be any Algorithm for Integer Programming with Quadratic Constraints
TLDR
It is shown that no computing device can be programmed to compute the optimum criterion value for all problems in this class of integer programming problems in which squares of variables may occur in the constraints.Abstract:
This paper studies a class of integer programming problems in which squares of variables may occur in the constraints, and shows that no computing device can be programmed to compute the optimum criterion value for all problems in this class.read more
Citations
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Journal ArticleDOI
Mixed-integer nonlinear optimization
TL;DR: An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.
Journal ArticleDOI
Non-convex mixed-integer nonlinear programming: A survey
Samuel Burer,Adam N. Letchford +1 more
TL;DR: In this paper, the authors survey the literature on non-convex mixed-integer nonlinear programs, discussing applications, algorithms, and software, and special attention is paid to the case in which the objective and constraint functions are quadratic.
Book ChapterDOI
Algorithms and Software for Convex Mixed Integer Nonlinear Programs
TL;DR: This paper provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables.
Book ChapterDOI
Nonlinear Integer Programming
TL;DR: This chapter is a study of a simple version of general nonlinear integer problems, where all constraints are still linear, and focuses on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure.
Journal ArticleDOI
Convex separable optimization is not much harder than linear optimization
TL;DR: A general-purpose algorithm for converting procedures that solves linear programming problems that is polynomial for constraint matrices with polynomially bounded subdeterminants and an algorithm for finding a ε-accurate optimal continuous solution to the nonlinear problem.
References
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Journal ArticleDOI
Theory of Recursive Functions and Effective Computability.
Solomon Feferman,Hartley Rogers +1 more
TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.
Journal ArticleDOI
The Decision Problem for Exponential Diophantine Equations
Journal ArticleDOI
The Decision Problem for Exponential Diophantine Equations
Journal ArticleDOI