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We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.…
We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on…
This paper presents a model-free reinforcement learning (RL) algorithm to solve the risk-averse optimal control (RAOC) problem for discrete-time nonlinear systems. While successful RL algorithms have been presented to learn optimal control…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…
Intensity modulated radiotherapy (IMRT) is one of the most common modalities for treating cancer patients. One of the biggest challenges is precise treatment delivery that accounts for varying motion patterns originating from…
Purpose:The recently proposed IPO-IMPT framework allows simultaneous optimization of dose, dose rate, and LET for FLASH treatment planning. Finding solutions to IPO-IMPT is difficult due to computational intensiveness. Nevertheless, an…
In computational pathology, cancer grading has been mainly studied as a categorical classification problem, which does not utilize the ordering nature of cancer grades such as the higher the grade is, the worse the cancer is. To incorporate…
Microarray gene expression data-based tumor classification is an active and challenging issue. In this paper, an integrated tumor classification framework is presented, which aims to exploit information in existing available samples, and…
We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four…
Denoising diffusion probabilistic models (DDPM) have shown remarkable performance in unconditional image generation. However, due to the stochasticity of the generative process in DDPM, it is challenging to generate images with the desired…
Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…
Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…
Using inverse planning tools to create radiotherapy treatment plans is an iterative process, where clinical trade-offs are explored by changing the relative importance of different objectives and rerunning the optimizer until a desirable…
Radiotherapy (RT) planning is complex, subjective, and time-intensive. Advances with artificial intelligence (AI) promise to improve its precision and efficiency, but progress is often limited by the scarcity of large, standardized…
This paper studies mean-risk portfolio optimization models using the conditional value-at-risk (CVaR) as a risk measure. We also employ a cardinality constraint for limiting the number of invested assets. Solving such a…
The modern workflow for radiation therapy treatment planning involves mathematical optimization to determine optimal treatment machine parameters for each patient case. The optimization problems can be computationally expensive, requiring…
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…