Convex optimization

About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.

Image Superresolution Using Support Vector Regression

Abstract: A thorough investigation of the application of support vector regression (SVR) to the superresolution problem is conducted through various frameworks. Prior to the study, the SVR problem is enhanced by finding the optimal kernel. This is done by formulating the kernel learning problem in SVR form as a convex optimization problem, specifically a semi-definite programming (SDP) problem. An additional constraint is added to reduce the SDP to a quadratically constrained quadratic programming (QCQP) problem. After this optimization, investigation of the relevancy of SVR to superresolution proceeds with the possibility of using a single and general support vector regression for all image content, and the results are impressive for small training sets. This idea is improved upon by observing structural properties in the discrete cosine transform (DCT) domain to aid in learning the regression. Further improvement involves a combination of classification and SVR-based techniques, extending works in resolution synthesis. This method, termed kernel resolution synthesis, uses specific regressors for isolated image content to describe the domain through a partitioned look of the vector space, thereby yielding good results

Output Reachable Set Estimation and Verification for Multilayer Neural Networks

Abstract: In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, and for a class of MLPs whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of the proposed approaches.

Received Signal Strength-Based Wireless Localization via Semidefinite Programming: Noncooperative and Cooperative Schemes

Abstract: The received signal strength (RSS)-based approach to wireless localization offers the advantage of low cost and easy implementability. To circumvent the nonconvexity of the conventional maximum likelihood (ML) estimator, in this paper, we propose convex estimators specifically for the RSS-based localization problems. Both noncooperative and cooperative schemes are considered. We start with the noncooperative RSS-based localization problem and derive a nonconvex estimator that approximates the ML estimator but has no logarithm in the residual. Next, we apply the semidefinite relaxation technique to the derived nonconvex estimator and develop a convex estimator. To further improve the estimation performance, we append the ML estimator to the convex estimator with the result by the convex estimator as the initial point. We then extend these techniques to the cooperative localization problem. The corresponding Cramer-Rao lower bounds (CRLB) are derived as performance benchmarks. Our proposed convex estimators comply well with the RSS measurement model, and simulation results clearly demonstrate their superior performance for RSS-based wireless localization.

Model Predictive Control of Swarms of Spacecraft Using Sequential Convex Programming

Abstract: DOI: 10.2514/1.G000218 This paper presents a decentralized, model predictive control algorithm for the optimal guidance and reconfiguration of swarms of spacecraft composed of hundreds to thousands of agents with limited capabilities. In previous work, J2-invariantorbitshavebeenfoundtoprovidecollision-freemotionforhundredsoforbitsinalowEarthorbit. This paper develops real-time optimal control algorithms for the swarm reconfiguration that involve transferring from one J2-invariant orbit to another while avoidingcollisions and minimizing fuel. The proposedmodel predictive control-sequential convex programming algorithm uses sequential convex programming to solve a series of approximate path planning problems until the solution converges. By updating the optimal trajectories during the reconfiguration, the model predictive control algorithm results in decentralized computations and communication between neighboring spacecraft only. Additionally, model predictive control reduces the horizon of the convex optimizations, which reduces the run time of the algorithm. Multiple time steps, time-varying collision constraints, and communication requirements are developed to guarantee stability, feasibility, and robustness of the model predictive control-sequential convex programming algorithm.

Solving convex programs by random walks

Abstract: Minimizing a convex function over a convex set in n-dimensional space is a basic, general problem with many interesting special cases. Here, we present a simple new algorithm for convex optimization based on sampling by a random walk. It extends naturally to minimizing quasi-convex functions and to other generalizations.