Related papers: Optimal bounds and extremal trajectories for time …
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is…
A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary…
We prove averaging theorems for ordinary differential equations and retarded functional differential equations. Our assumptions are weaker than those required in the results of the existing literature. Usually, we require that the…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
This paper considers time-average optimization, where a decision vector is chosen every time step within a (possibly non-convex) set, and the goal is to minimize a convex function of the time averages subject to convex constraints on these…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…