Deterministic Global Optimization with Artificial Neural Networks Embedded

Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and … Read more

SDDP.jl: a Julia package for Stochastic Dual Dynamic Programming

In this paper we present SDDP.jl, an open-source library for solving multistage stochastic optimization problems using the Stochastic Dual Dynamic Programming algorithm. SDDP.jl is built upon JuMP, an algebraic modelling language in Julia. This enables a high-level interface for the user, while simultaneously providing performance that is similar to implementations in low-level languages. We benchmark … Read more

Optimality Conditions and Constraint Qualifications for Generalized Nash Equilibrium Problems and their Practical Implications

Generalized Nash Equilibrium Problems (GNEPs) are a generalization of the classic Nash Equilibrium Problems (NEPs), where each player’s strategy set depends on the choices of the other players. In this work we study constraint qualifications and optimality conditions tailored for GNEPs and we discuss their relations and implications for global convergence of algorithms. Surprisingly, differently … Read more

The SCIP Optimization Suite 5.0

This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over … Read more

Load Scheduling for Residential Demand Response on Smart Grids

The residential load scheduling problem is concerned with finding an optimal schedule for the operation of residential loads so as to minimize the total cost of energy while aiming to respect a prescribed limit on the power level of the residence. We propose a mixed integer linear programming formulation of this problem that accounts for … Read more

Reducing conservatism in Robust Optimization

Although Robust Optimization is a powerful technique in dealing with uncertainty in optimization, its solutions can be too conservative when it leads to an objective value much worse than the nominal solution or even to infeasibility of the robust problem. In practice, this can lead to robust solutions being disregarded in favor of the nominal … Read more

A decentralized framework for the optimal coordination of distributed energy resources

Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous Distributed Energy Resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig-Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within … Read more

A class of spectral bounds for Max k-cut

In this paper we introduce a new class of bounds for the maximum -cut problem on undirected edge-weighted simple graphs. The bounds involve eigenvalues of the weighted adjacency matrix together with geometrical parameters. They generalize previous results on the maximum (2-)cut problem and we demonstrate that they can strictly improve over other eigenvalue bounds from … Read more

Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more

A transformation-based discretization method for solving general semi-infinite optimization problems

Discretization methods are commonly used for solving standard semi-infinite optimization (SIP) problems. The transfer of these methods to the case of general semi-infinite optimization (GSIP) problems is difficult due to the $x$-dependence of the infinite index set. On the other hand, under suitable conditions, a GSIP problem can be transformed into a SIP problem. In … Read more