We present GALINI, an open source solver for nonconvex mixed-integer quadratically-constrained quadratic programs formulated with the Python algebraic modeling library Pyomo. GALINI uses Pyomo to represent optimization problems and leverages the existing library ecosystem to implement different parts of the solver. GALINI includes a generic branch \& bound algorithm that can be use develop new … Read more
The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modeling. In this paper we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a … Read more
Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed-integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes … Read more
In this paper, we propose and study a distributed and secure algorithm for computing dominant (or truncated) singular value decompositions (SVD) of large and distributed data matrices. We consider the scenario where each node privately holds a subset of columns and only exchanges “safe” information with other nodes in a collaborative effort to calculate a … Read more
LSP(n), the largest small polygon with n vertices, is the polygon of unit diameter that has maximal area A(n). It is known that for all odd values n≥3, LSP(n) is the regular n-polygon; however, this statement is not valid for even values of n. Finding the polygon LSP(n) and A(n) for even values n≥6 has … Read more
We present JuDGE.jl, an open-source Julia package for solving multistage stochastic capacity expansion problems using Dantzig-Wolfe decomposition. Models for JuDGE.jl are built using JuMP, the algebraic modelling language in Julia, and solved by repeatedly applying mixed-integer programming. We illustrate JuDGE.jl by formulating and solving a toy knapsack problem, and demonstrate the performance of JuDGE.jl on … Read more
In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more
In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more
This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems … Read more
It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more