Related papers: Rowing and the Same-Sum Problem Have Their Moments
The power flow equations model the steady-state relationship between the power injections and voltage phasors in an electric power system. By separating the real and imaginary components of the voltage phasors, the power flow equations can…
This paper focuses on the problem of determining a minimum-cost fleet of battery electric ships for a given liner shipping operation. The problem is strongly nonlinear and includes integer-valued decision variables, which make it…
The search heuristics Tabu search and Simulated annealing are commonly used meta-heuristics. The two heuristics have different ways of ensuring diversification. The heuristics can be implemented for solving the stowage planning problem. The…
In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of…
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution focuses on the case of non-compact control sets. We describe a…
In this paper, we consider the gathering problem of seven autonomous mobile robots on triangular grids. The gathering problem requires that, starting from any connected initial configuration where a subgraph induced by all robot nodes…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
This paper proposes a spatial-temporal recurrent neural network architecture for deep $Q$-networks that can be used to steer an autonomous ship. The network design makes it possible to handle an arbitrary number of surrounding target ships…
Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…
Random reshuffling with momentum (RRM) corresponds to the SGD optimizer with momentum option enabled, as found in many machine learning libraries like PyTorch and TensorFlow. Despite its widespread use, the convergence properties of RRM do…
The properties of value functions of time inhomogeneous optimal stopping problem and zero-sum game (Dynkin game) are studied through time dependent Dirichlet form. Under the absolute continuity condition on the transition function of the…
Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…
The confrontation of modern intelligence is to some extent a non-complete information confrontation, where neither side has access to sufficient information to detect the deployment status of the adversary, and then it is necessary for the…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…
Gathering mobile robots is a widely studied problem in robotic research. This survey first introduces the related work, summarizing models and results. Then, the focus shifts on the open problem of gathering fat robots. In this context,…
A mediator observes no-regret learners playing an extensive-form game repeatedly across $T$ rounds. The mediator attempts to steer players toward some desirable predetermined equilibrium by giving (nonnegative) payments to players. We call…
We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the…
We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal…
We consider online content recommendation with implicit feedback through pairwise comparisons, formalized as the so-called dueling bandit problem. We study the dueling bandit problem in the Condorcet winner setting, and consider two notions…