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Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
We propose a homotopy method for solving mathematical programs with complementarity constraints (CCs). The indicator function of the CCs is relaxed by a Lasry-Lions double envelope, an extension of the Moreau envelope that enjoys an…
We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
In the article the problem of output setpoint tracking for affine non-linear system is considered. Presented approach combines state feedback linearization and homotopy numerical continuation in subspaces of phase space where feedback…
Trained humans exhibit highly agile spatial skills, enabling them to operate vehicles with complex dynamics in demanding tasks and conditions. Prior work shows that humans achieve this performance by using strategies such as satisficing,…
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…
We present a first-order method for solving constrained optimization problems. The method is derived from our previous work, a modified search direction method inspired by singular value decomposition. In this work, we simplify its…
We study last-iterate convergence properties of algorithms for solving two-player zero-sum games based on Regret Matching$^+$ (RM$^+$). Despite their widespread use for solving real games, virtually nothing is known about their last-iterate…
Continuous amortization is a technique for computing the complexity of algorithms, and it was first presented by the author in Burr, Krahmer, & Yap (2009). Continuous amortization can result in simpler and more straight-forward complexity…
This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient…
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton's method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality…
We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration,…
Legged robotic systems can play an important role in real-world applications due to their superior load-bearing capabilities, enhanced autonomy, and effective navigation on uneven terrain. They offer an optimal trade-off between mobility…
We study deception in adversarial graph traversal, where a mobile agent seeks to reach a goal with minimum cost while an adversary alters edge costs to increase the total traversal cost. Unlike prior works that assume fixed…
We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent…
We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for…
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…