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We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work shows that nonsymmetric DPP (NDPP) kernels have significant…

Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…

In this paper we address a practical aspect of differential barrier penalty functions in linear programming. In this respect we propose an affine scaling interior point algorithm based on a large classe of differential barrier functions.…

Multi-stage decision problems under uncertainty can be efficiently solved with the Stochastic Dual Dynamic Programming (SDDP) algorithm. However, traditional implementations require all stage problems to be feasible. Feasibility is usually…

To address the limitations of existing magnitude-based pruning algorithms in cases where model weights or activations are of large and similar magnitude, we propose a novel perspective to discover parameter redundancy among channels and…

The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate…

We design nearly-linear time numerical algorithms for the problem of multivariate multipoint evaluation over the fields of rational, real and complex numbers. We consider both \emph{exact} and \emph{approximate} versions of the algorithm.…

The existence of large volumes of time series data in many applications has motivated data miners to investigate specialized methods for mining time series data. Clustering is a popular data mining method due to its powerful exploratory…

Neural networks performance has been significantly improved in the last few years, at the cost of an increasing number of floating point operations per second (FLOPs). However, more FLOPs can be an issue when computational resources are…

Achieving a balance between accuracy and efficiency is a critical challenge in facial landmark detection (FLD). This paper introduces Parallel Optimal Position Search (POPoS), a high-precision encoding-decoding framework designed to address…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…

Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off…

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often…

Mitosis nuclei count is one of the important indicators for the pathological diagnosis of breast cancer. The manual annotation needs experienced pathologists, which is very time-consuming and inefficient. With the development of deep…