A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering they are taking their current … Read more

Data Collaboration Analysis Over Matrix Manifolds

The effectiveness of machine learning (ML) algorithms is deeply intertwined with the quality and diversity of their training datasets. Improved datasets, marked by superior quality, enhance the predictive accuracy and broaden the applicability of models across varied scenarios. Researchers often integrate data from multiple sources to mitigate biases and limitations of single-source datasets. However, this … Read more

Uncertainty Quantification for Multiobjective Stochastic Convex Quadratic Programs

A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more

On Coupling Constraints in Linear Bilevel Optimization

It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and without coupling constraints w.r.t. their complexity-theoretical hardness. In this note, we prove that, although there is a clear difference between these … Read more

Solution methods for partial inverse combinatorial optimization problems in which weights can only be increased

Partial inverse combinatorial optimization problems are bilevel optimization problems in which the leader aims to incentivize the follower to include a given set of elements in the solution of their combinatorial problem. If the set of required elements defines a complete follower solution, the inverse combinatorial problem is solvable in polynomial time as soon as … Read more

Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

Risk-averse multi-stage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage … Read more

A Hybrid Genetic Algorithm for Generalized Order Acceptance and Scheduling

In this paper, a novel approach is presented to address a challenging optimization problem known as Generalized Order Acceptance Scheduling. This problem involves scheduling a set of orders on a single machine with release dates, due dates, deadlines, and sequence-dependent setup times judiciously to maximize revenue. In view of resource constraints, not all orders can … Read more

Kantorovich and Zalgaller (1951): the 0-th Column Generation Algorithm

This article delves into the early development of the Column Generation technique. It begins with Kantorovich’s classic 1939 work, correcting widespread misconceptions about his contributions to the Cutting Stock Problem. Then, it brings to light Kantorovich and Zalgaller’s lesser-known 1951 book, which is revealed to contain a complete Column Generation algorithm. The article also places … Read more

The convergence rate of the Sandwiching algorithm for convex bounded multiobjective optimization

Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … Read more

Addressing Hierarchical Jointly-Convex Generalized Nash Equilibrium Problems with Nonsmooth Payoffs

We consider a Generalized Nash Equilibrium Problem whose joint feasible region is implicitly defined as the solution set of another Nash game. This structure arises e.g. in multi-portfolio selection contexts, whenever agents interact at different hierarchical levels. We consider nonsmooth terms in all players’ objectives, to promote, for example, sparsity in the solution. Under standard … Read more