Related papers: A Sequential Quadratic Programming Approach to the…
In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…
The multi-cluster games are addressed in this paper, where all players team up with the players in the cluster that they belong to, and compete against the players in other clusters to minimize the cost function of their own cluster. The…
Trajectory planning for autonomous race cars poses special challenges due to the highly interactive and competitive environment. Prior work has applied game theory as it provides equilibria for such non-cooperative dynamic problems. This…
This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
This paper presents a pioneering investigation into discrete-time two-person non-zero-sum linear quadratic (LQ) stochastic games with random coefficients. We derive necessary and sufficient conditions for the existence of open-loop Nash…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash…
The Nash Equilibrium (NE), one of the elegant and fundamental concepts in game theory, plays a crucial part within various fields, including engineering and computer science. However, efficiently computing an NE in normal-form games remains…
Sequential quadratic programming (SQP) methods have been remarkably successful in solving a broad range of nonlinear optimization problems. These methods iteratively construct and solve quadratic programming (QP) subproblems to compute…
In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or…
To facilitate effective, safe deployment in the real world, individual robots must reason about interactions with other agents, which often occur without explicit communication. Recent work has identified game theory, particularly the…
For the characterization of Feedback Nash Equilibria (FNE) in linear quadratic games, this paper provides a detailed analysis of the discrete-time discounted coupled best-response equations for the scalar two-player setting, together with a…
We consider dynamic games defined over an infinite horizon, characterized by linear, discrete-time dynamics and quadratic cost functionals. Considering such linear-quadratic (LQ) dynamic games, we focus on their solutions in terms Nash…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
In this paper, we investigate distributed generalized Nash equilibrium (GNE) computation of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of…
This paper investigates online stochastic aggregative games subject to local set constraints and time-varying coupled inequality constraints, where each player possesses a time-varying expectation-valued cost function relying on not only…
In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion…
Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to…
In this work, we investigate the distributed generalized Nash equilibrium (GNE) seeking problems for $N$-coalition games with inequality constraints. First, we study the scenario where each agent in a coalition has full information of all…