Related papers: Continuation Path Learning for Homotopy Optimizati…
Hyperparameter optimization (HPO) is generally treated as a bi-level optimization problem that involves fitting a (probabilistic) surrogate model to a set of observed hyperparameter responses, e.g. validation loss, and consequently…
Imaging Inverse problems aim to reconstruct an underlying image from undersampled, coded, and noisy observations. Within the wide range of reconstruction frameworks, the unrolling algorithm is one of the most popular due to the synergistic…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
Alternating-Current Optimal Power Flow (AC-OPF) is framed as a NP-hard non-convex optimization problem that solves for the most economical dispatch of grid generation given the AC-network and device constraints. Although there are no…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose…
In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints…
Multi-agent trajectory planning requires ensuring both safety and efficiency, yet deadlocks remain a significant challenge, especially in obstacle-dense environments. Such deadlocks frequently occur when multiple agents attempt to traverse…
Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this…
Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF…
Alternating-Current Optimal Power Flow (AC-OPF) is an optimization problem critical for planning and operating the power grid. The problem is traditionally formulated using only continuous variables. Typically, control devices with…
Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…