An exponential cone representation of the general power cone

Chandrasekaran and Shah (2017) used the exponential cone to model the second-order cone in demonstration of its modeling capabilities. We simplify and extend this result to general power cones. Article Download View An exponential cone representation of the general power cone

solar: A solar thermal power plant simulator for blackbox optimization benchmarking

This work introduces solar, a collection of  ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present different design aspects of a concentrated solar power plant simulated by blackbox numerical models. The type of variables (discrete or continuous), dimensionality, and number and types of constraints (including hidden constraints)  differ across instances. Some are deterministic, others are stochastic … Read more

Nonconvex optimization problems involving the Euclidean norm: Challenges, progress, and opportunities

The field of global optimization has advanced significantly over the past three decades. Yet, the solution of even small instances of many nonconvex optimization problems involving the Euclidean norm to global optimality remains beyond the reach of modern global optimization methods. These problems include numerous well-known and high-impact open research questions from a diverse collection … Read more

Edge expansion of a graph: SDP-based computational strategies

Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant for any graph. The first variant uses the SDP relax- ation first to reduce the search space considerably. One … Read more

A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm

For continuous decision spaces, nonlinear programs (NLPs) can be efficiently solved via sequential quadratic programming (SQP) and, more generally, sequential convex programming (SCP). These algorithms linearize only the nonlinear equality constraints and keep the outer convex structure of the problem intact, such as (conic) inequality constraints or convex objective terms. The aim of the presented … Read more

Certified Constraint Propagation and Dual Proof Analysis in a Numerically Exact MIP Solver

This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while sacrificing as little computational performance as possible in comparison to a pure floating-point implementation. The study also addresses the adaptation of certification … Read more

Similarity-based Decomposition Algorithm for Two-stage Stochastic Scheduling

This paper presents a novel decomposition method for two-stage stochastic mixed-integer optimization problems. The algorithm builds upon the idea of similarity between finite sample sets to measure how similar the first-stage decisions are among the uncertainty realization scenarios. Using such a Similarity Index, the non-anticipative constraints are removed from the problem formulation so that the … Read more

The MIP Workshop 2023 Computational Competition on Reoptimization

This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more

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

libDIPS — Discretization-Based Semi-Infinite and Bilevel Programming Solvers

We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … Read more