最优化与控制
We study a stochastic optimal control problem motivated by the operation of a large ensemble of residential storage devices coordinated by an energy aggregator. The aggregator remunerates prosumers in exchange for direct control of their…
The primal dual hybrid gradient algorithm (PDHG), which is also known as the Arrow-Hurwicz method, is a fundamental algorithm for saddle point problems especially in imaging. It also inspires a great number of influential algorithms such as…
In this paper, we introduce the notion of (strictly) semimonotone matrices of exact order $k$, where $0\leq k\leq n$, and explore their properties. We fully characterize the $3 \times 3$ (strictly) semimonotone matrices of exact order $2$,…
This article proposes an energy storage-enhanced hydrogen electrolyzer (ESEHE) to provide grid-forming (GFM) services for off-grid renewable power to hydrogen (ReP2H) systems. Unlike conventional ReP2H systems that use a centralized energy…
We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…
This paper investigates numerical solution methods for the Schatten-$p$ quasi-norm regularized problem with $p \in [0,1]$, which has been widely studied for finding low-rank solutions of linear inverse problems and gained successful…
We prove global stabilization of the marine riser models using a feedback controller that depend on finitely many finite-volume elements and finitely many nodal observables. Our approach is based on a feedback control design for dissipative…
The asymptotic behavior of the optimal TSP tour length is well known from the classical Beardwood--Halton--Hammersley theorem. We extend this result to the Traveling Salesman Problem with Drone (TSPD), a cooperative routing problem in which…
Gr\"unbaum's inequality guarantees that the centroid of a convex body has halfspace depth at least $1/e$: every halfspace containing the centroid captures at least a $1/e$ fraction of the body's volume. For mixed-integer convex sets…
One considers polynomial optimization problems with compact feasible set $\mathbf{\Omega}$ defined by SOS-concave polynomials $g_j$, and with a globally non-convex polynomial objective $f$. We show that if $f$ is strongly convex on…
This paper explores optimality conditions in optimization problems involving generalized invex fuzzy functions. We extend the classical KKT framework to settings in which the objective and constraint functions are nonsmooth, vector-valued,…
This paper introduces and solves the Generalized Heron-Waist Problem (GHWP), that integrates the classical Heron problem of optimal hub location and the waist problem of minimal-perimeter configuration. The GHWP seeks an optimal closed…
Existing multi-criteria decision-making (MCDM) methods often face challenges when evaluating a large number of alternatives, leading to skewed results in selecting the optimal choice. Similarly, conventional efficiency analysis (EA)…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
Dueling optimization considers optimizing an objective with access to only a comparison oracle of the objective function. It finds important applications in emerging fields such as recommendation systems and robotics. Existing works on…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Since the concept of input-to-state stability (ISS) was introduced, it has been extensively investigated for finite-dimensional control systems and has recently received attention for infinite-dimensional systems. While numerical techniques…
This work addresses minimum-weight design of undamped Euler-Bernoulli frame structures under subresonant single-frequency harmonic excitations, focusing on (robust) dynamic compliance and (robust) peak input power with ellipsoidal load…
We study infinite-horizon Markov Decision Processes (MDPs) with a continuum of heterogeneous agents interacting through a common noise, without assuming exchangeability. We introduce the framework of Conditional Non-Exchangeable Mean Field…
We study ratio-induced mismatch costs of the form $c(s,o)=J(\iota_S(s)/\iota_O(o))$, built from positive scale maps $\iota_S:S\to(0,\infty)$ and $\iota_O:O\to(0,\infty)$ and a penalty $J:(0,\infty)\to[0,\infty)$. Assuming inversion…