The SCIP Optimization Suite 9.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a … Read more

Strengthening SONC Relaxations with Constraints Derived from Variable Bounds

Nonnegativity certificates can be used to obtain tight dual bounds for polynomial optimization problems. Hierarchies of certificate-based relaxations ensure convergence to the global optimum, but higher levels of such hierarchies can become very computationally expensive, and the well-known sums of squares hierarchies scale poorly with the degree of the polynomials. This has motivated research into … Read more

Global Optimization of Mixed-Integer Nonlinear Programs with SCIP 8.0

For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that … Read more

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type … Read more

A Computational Study of Perspective Cuts

The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study … Read more

The SCIP Optimization Suite 7.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies … Read more

Invex Optimization Revisited

Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer. In this work, we provide necessary conditions for KT-invexity in n-dimensions and … Read more

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent … Read more