Related papers: Data-driven Projection Generation for Efficiently …
We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms.…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
We consider the problem of optimizing the interconnection graphs of complex networks to promote synchronization. When traditional optimization methods are inapplicable, due to uncertain or unknown node dynamics, we propose a data-driven…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
This work is the first to employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) towards learning a forward and an inverse solution operator of partial differential equations…
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a…
We consider the problem of computationally-efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods…
In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…