Related papers: Locally Feasibly Projected Sequential Quadratic Pr…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…
Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is…
Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes…