Related papers: Disciplined Biconvex Programming
This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a…
Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
This paper discusses the computational resolution and presents numerical results for solving affine combinations of Heaviside composite optimization problems (abbreviated as A-HSCOPs) by a progressive integer programming (abbreviated as…
This paper investigates the collaboration of multiple connected and automated vehicles (CAVs) in different scenarios. In general, the collaboration of CAVs can be formulated as a nonlinear and nonconvex model predictive control (MPC)…
This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
Fixed-point iterations are at the heart of numerical computing and are often a computational bottleneck in real-time applications that typically need a fast solution of moderate accuracy. We present neural fixed-point acceleration which…
Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the…
Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
Privacy has been a major motivation for distributed problem optimization. However, even though several methods have been proposed to evaluate it, none of them is widely used. The Distributed Constraint Optimization Problem (DCOP) is a…
This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…
Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…
The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…