Forward – Backward Greedy Algorithms for Atomic – Norm Regularization

In many signal processing applications, one aims to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as “atoms” allow us to define “atomic norms” that can be used to construct convex regularizers for the reconstruction problem. Efficient algorithms are available to … Read more

Minimal Points, Variational Principles, and Variable Preferences in Set Optimization

The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point … Read more

How important are branching decisions: fooling MIP solvers

We show the importance of selecting good branching variables by exhibiting a family of instances for which an optimal solution is both trivial to find and provably optimal by a fixed-size branch-and-bound tree, but for which state-of-the-art Mixed Integer Programming solvers need an increasing amount of resources. The instances encode the edge-coloring problem on a … Read more

Unit commitment with valve-point loading effect

Valve-point loading affects the input-output characteristics of generating units, bringing the fuel costs nonlinear and nonsmooth. This has been considered in the solution of load dispatch problems, but not in the planning phase of unit commitment. This paper presents a mathematical optimization model for the thermal unit commitment problem considering valve-point loading. The formulation is … Read more

Convergence Rates with Inexact Nonexpansive Operators

In this paper, we present a convergence rate analysis for the inexact Krasnosel’ski{\u{\i}}-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity bounds, and then, under a metric subregularity assumption, we establish local linear convergence for the distance of the iterates to the set of … Read more

Approximating Pareto Curves using Semidefinite Relaxations

We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{x \in S} \{(f_1(x),f_2(x))\}$, where $f_1$ and $f_2$ are two conflicting positive polynomial criteria and $S \subset R^n$ is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start … Read more

Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques

A reformulation of quadratically constrained binary programs as duals of set-copositive linear optimization problems is derived using either \(\{0,1\}\)-formulations or \(\{-1,1\}\)-formulations. The latter representation allows an extension of the randomization technique by Goemans and Williamson. An application to the max-clique problem shows that the max-clique problem is equivalent to a linear program over the max-cut … Read more

Parallel Large-Neighborhood Search Techniques for LNG Inventory Routing

Liquefied natural gas (LNG) is estimated to account for a growing portion of the world natural gas trade. For profitable operation of a capital intensive LNG project, it is necessary to optimally design various aspects of the supply chain associated with it. Of particular interest is optimization of ship schedules and the inventories on the … Read more

An inertial alternating direction method of multipliers

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we investigate into detail. To this aim we make use of the inertial version of the Douglas-Rachford splitting method for monotone … Read more

Modal occupation measures and LMI relaxations for nonlinear switched systems control

This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of Hamilton-Jacobi-Bellman inequalities is also characterized. The LPs … Read more