Related papers: KKT-Informed Neural Network
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we…
The KKT optimality conditions for multi-objective interval-valued optimization problem on Hadamard manifold are studied in this paper. Several concepts of Pareto optimal solutions, considered under LU and CW ordering on the class of all…
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…
We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear…
Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…
Training of neural networks amounts to nonconvex optimization problems that are typically solved by using backpropagation and (variants of) stochastic gradient descent. In this work we propose an alternative approach by viewing the training…
The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…
Distribution network reconfiguration (DNR) is an effective approach for optimizing distribution network operation. However, the DNR problem is computationally challenging due to the mixed-integer non-convex nature. One feasible approach for…
In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi…
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Sensor networks play a critical role in many situational awareness applications. In this paper, we study the problem of determining sensor placements to balance coverage and connectivity objectives over a target region. Leveraging algebraic…
In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of…
Pre-trained models are widely used in fine-tuning downstream tasks with linear classifiers optimized by the cross-entropy loss, which might face robustness and stability problems. These problems can be improved by learning representations…
Adversarial perturbations have drawn great attentions in various machine learning models. In this paper, we investigate the sample adversarial perturbations for nonlinear support vector machines (SVMs). Due to the implicit form of the…
This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…