最优化与控制
This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash…
We develop a novel primal heuristic for nonconvex Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs). The method is built around a convex approximation that is dynamically adjusted within a feasibility-pump-style…
We consider the problem of simultaneous control and parameter estimation when the model is available only as a differentiable physics simulator. We propose a receding-horizon control framework in which a model predictive control (MPC)…
Standard chance constrained control algorithms typically rely on the assumption that uncertainties in vehicle states obey Gaussian statistics. Highly nonlinear systems tend to disrupt Gaussianity, challenging standard chance-constrained…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
This paper presents a smooth parameterization of continuous-time Signal Temporal Logic (CT-STL) specifications for nonconvex trajectory optimization that is sound and complete up to the accuracy of the underlying numerical integration…
In this paper, we investigate the behavior of the family of graph-based splitting algorithms specialized to the problem of finding a point in the intersection of linear subspaces. The algorithms in this family, which encompasses several…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
We show optimal triangulations for piecewise linear (PWL) approximations of indefinite quadratic functions over the plane. Optimal triangulations have minimum triangle density while allowing a PWL approximation that fulfills a prescribed…
In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic…
In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into…
Deterministic global optimization of nonlinear models is important in many scientific and engineering applications. This framework typically involves repeatedly solving convex relaxations of the nonconvex problem, meaning that the strength…
This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on…
Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming…
We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolved. We determine its exact maximal quantum value and show…
Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed…
Fr\'echet regression, or conditional Barycenters, is a flexible framework for modeling relationships between covariates (usually Euclidean) and response variables on general metric spaces, e.g., probability distributions or positive…
In the electric system, extreme weather events can cause trips or physical damage to transmission lines, leading to large-scale load shedding. To mitigate power shedding, we propose a framework that pre-positions the commitment of…