Related papers: BPQP: A Differentiable Convex Optimization Framewo…

Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…

Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization…

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…

In the predict-then-optimize framework, the objective is to train a predictive model, mapping from environment features to parameters of an optimization problem, which maximizes decision quality when the optimization is subsequently solved.…

Many tasks in deep learning involve optimizing over the \emph{inputs} to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially…

Balancing convergence speed, generalization capability, and computational efficiency remains a core challenge in deep learning optimization. First-order gradient descent methods, epitomized by stochastic gradient descent (SGD) and Adam,…

Sequential learning systems are used in a wide variety of problems from decision making to optimization, where they provide a 'belief' (opinion) to nature, and then update this belief based on the feedback (result) to minimize (or maximize)…

Obstacle avoidance is a fundamental vision-based task essential for enabling quadrotors to perform advanced applications. When planning the trajectory, existing approaches both on optimization and learning typically regard quadrotor as a…

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…

Differentiating through the solution of a quadratic program (QP) is a central problem in differentiable optimization. Most existing approaches differentiate through the Karush--Kuhn--Tucker (KKT) system, but their computational cost and…

Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn…

Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…

Optimizing deep learning models is generally performed in two steps: (i) high-level graph optimizations such as kernel fusion and (ii) low level kernel optimizations such as those found in vendor libraries. This approach often leaves…

Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…

Backpropagation (BP) is the cornerstone of today's deep learning algorithms, but it is inefficient partially because of backward locking, which means updating the weights of one layer locks the weight updates in the other layers.…