Sensitivity analysis of semidefinite programs without strong duality

Suppose that we are given a feasible conic program with a finite optimal value and with strong duality failing. It is known that there are small perturbations of the problem data that lead to relatively big changes in the optimal value. We quantify the notion of big change in the case of a semidefinite program … Read more

A Non-Parametric Structural Hybrid Modeling Approach for Electricity Prices

We develop a stochastic model of zonal/regional electricity prices, designed to reflect information in fuel forward curves and aggregated capacity and load as well as zonal or regional price spreads. We use a nonparametric model of the supply stack that captures heat rates and fuel prices for all generators in the market operator territory, combined … Read more

iPiano: Inertial Proximal Algorithm for Nonconvex Optimization

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm … Read more

Projection Methods: An Annotated Bibliography of Books and Reviews

Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative algorithms that use projections onto sets while relying on the general principle that when a family … Read more

Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation

The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this paper the extension of the classical Levenberg-Marquardt algorithm to the scenarios where the linearized least squares subproblems are solved inexactly and/or the gradient model is … Read more

Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build … Read more

A Parallel Local Search Framework for the Fixed-Charge Multicommodity Network Flow Problem

We present a parallel local search approach for obtaining high quality solutions to the Fixed Charge Multi-commodity Network Flow problem (FCMNF). The approach proceeds by improving a given feasible solution by solving restricted instances of the problem where flows of certain commodities are fixed to those in the solution while the other commodities are locally … Read more

How Difficult is Nonlinear Optimization? A Practical Solver Tuning Approach, with Illustrative Results

Nonlinear optimization (NLO) per definitionem covers a vast range of problems, from trivial to practically intractable. For this reason, it is impossible to offer “guaranteed” advice to NLO software users. This fact becomes especially obvious, when facing unusually hard and/or previously unexplored NLO challenges. In the present study we offer some related practical observations, propose … Read more

Steplength Thresholds for Invariance Preserving of Discretization Methods of Dynamical Systems on a Polyhedron

Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically … Read more

On Lipschitz optimization based on gray-box piecewise linearization

We address the problem of minimizing objectives from the class of piecewise differentiable functions whose nonsmoothness can be encapsulated in the absolute value function. They possess local piecewise linear approximations with a discrepancy that can be bounded by a quadratic proximal term. This overestimating local model is continuous but generally nonconvex. It can be generated … Read more