Repository – Page 103 – Optimization Online

Hub Network Design Problem with Capacity, Congestion and Stochastic Demand Considerations

Published: 2021/12/19, Updated: 2023/08/07

We introduce the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decision and congestion cost effect into the problem and allowing dynamic routing for origin-destination pairs. Connecting strategic and operational level decisions, … Read more

Mean-Covariance Robust Risk Measurement

Published: 2021/12/19

Viet Anh Nguyen

Soroosh Shafieezadeh-Abadeh

Damir Filipovic

Daniel Kuhn

Finance and Economics, Robust Optimization, Stochastic Programming risk measurement, robust optimization

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. … Read more

Risk-Averse Stochastic Optimal Control: an efficiently computable statistical upper bound

Published: 2021/12/17, Updated: 2022/04/19

Vincent Guigues

Alexander Shapiro

Yi Cheng

Stochastic Programming dynamic programming, risk measures, sddp, statistical upper bounds, stochastic optimal control, stochastic programming

In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of … Read more

New interior-point approach for one- and two-class linear support vector machines using multiple variable splitting

Published: 2021/12/17

Jordi Castro

Data-Mining, Linear, Cone and Semidefinite Programming interior point methods, large-scale optimization, multiple variable splitting, one-class support vector machine, support vector classifier

Multiple variable splitting is a general technique for decomposing problems by using copies of variables and additional linking constraints that equate their values. The resulting large optimization problem can be solved with a specialized interior-point method that exploits the problem structure and computes the Newton direction with a combination of direct and iterative solvers (i.e., … Read more

Distributionally risk-receptive and risk-averse network interdiction problems with general ambiguity set

Published: 2021/12/16, Updated: 2022/06/11

Sumin Kang

Manish Bansal

Nonlinear Optimization, Stochastic Programming decomposition algorithm, distributionally risk-receptive, distributionally robust optimization, general ambiguity set, stochastic network interdiction

We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk-averse (or robust) network interdiction problem (DRA-NIP) and a distributionally risk-receptive network interdiction problem (DRR-NIP) where a leader maximizes a follower’s minimal expected objective value for either the worst-case or the best-case, respectively, probability distribution belonging to ambiguity set … Read more

The SCIP Optimization Suite 8.0

Published: 2021/12/16, Updated: 2022/01/31

Jasper van Doornmalen

Branch and Cut Algorithms, Integer Programming, Optimization Software and Modeling Systems branch-and-cut, branch-and-price, column generation, constraint integer programming, linear programming, mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer semidefinite programming, optimization solver, parallelization

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type … Read more

A unified analysis of descent sequences in weakly convex optimization, including convergence rates for bundle methods

Published: 2021/12/15, Updated: 2022/06/23

Complementarity and Variational Inequalities, Nonlinear Optimization bundle methods, descent methods, error bound, linear convergence, model-based methods, proximal descent, proximal gradient method, weak convexity

We present a framework for analyzing convergence and local rates of convergence of a class of descent algorithms, assuming the objective function is weakly convex. The framework is general, in the sense that it combines the possibility of explicit iterations (based on the gradient or a subgradient at the current iterate), implicit iterations (using a … Read more

Bayesian Distributionally Robust Optimization

Published: 2021/12/15, Updated: 2023/02/08

Alexander Shapiro

Enlu Zhou

Yifan Lin

Robust Optimization, Stochastic Programming

We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO approaches in the use of Bayesian estimation of the unknown distribution. To make computation of Bayesian updating tractable, Bayesian-DRO first assumes the underlying distribution takes a parametric … Read more

A nested primal–dual FISTA-like scheme for composite convex optimization problems

Published: 2021/12/14, Updated: 2022/08/05

Silvia Bonettini

Marco Prato

Simone Rebegoldi

Convex Optimization, Nonsmooth Optimization convex optimization, forward--backward algorithms, image deblurring, inertial techniques, primal-dual algorithms

We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” … Read more

A covering decomposition algorithm for power grid cyber-network segmentation

Published: 2021/12/13

Applications - OR and Management Sciences defender-attacker-defender, interdiction, mixed-integer programming, power networks, security, trilevel optimization

We present a trilevel interdiction model for optimally segmenting the Supervisory Control and Data Acquisition (SCADA) network controlling an electric power grid. In this formulation, we decide how to partition nodes of the SCADA network in order to minimize the shedding of load from a worst-case cyberattack, assuming that the grid operator has the opportunity … Read more