We analyze the computational complexity of the synthesis problem of decentralized energy systems. This synthesis problem consists of combining various types of energy conversion units and determining their sizing as well as operations in order to meet time-varying energy demands while maximizing an objective function, e.g., the net present value. In this paper, we prove … Read more
We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products meeting given attribute percentage requirements. Our relaxations are derived by considering a set which arises from the formulation by … Read more
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
We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart problem retains the … Read more
We show that the evolution of a dynamical system driven by controls obtained by the solution of an embedded optimization problem (as done in MPC) can be cast as a differential variational inequality (DVI). The DVI abstraction reveals that standard sampled-data MPC implementations (in which the control law is computed using states that are sampled … Read more
Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced … Read more
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to … Read more
The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The rst one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The … Read more
This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description … Read more
Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NP- hard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and bi- nary variables … Read more