A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm

The role of optimization in both engineering analysis and designis continually expanding. As such, faster and more powerful optimization algorithms are in constant demand. In this dissertation, motivated by problems from engineering analysis and design, new Sequential Quadratic Programming (SQP) algorithms generating feasible iterates are described and analyzed. What distinguishes these algorithms from previous feasible SQP algorithms is a dramatic reduction in the amount of computation required to generate a new iterate while still enjoying the same global and fast local convergence properties.First, a basic algorithm which solves the standard smooth inequality constrained nonlinear programming problem is considered. The main idea involves a simple perturbation of the Quadratic Program (QP) for the standard SQP search direction. The perturbation has the property that a feasible direction is always obtained and fast local convergence is preserved. An extension of the basic algorithm is then proposed which solves the inequality constrained mini-max problem. The algorithm exploits the special structure of the problem and is shown to have the same global and local convergence properties as the basic algorithm.Next, the algorithm is extended to efficiently solve problems with very many objective and/or constraint functions. Such problems often arise in engineering design as, e.g., discretized Semi-Infinite Programming (SIP) problems. The key feature of the extension is that only a small subset of the objectives and constraints are used to generate a search directionat each iteration. The result is much smaller QP sub-problems and fewer gradient evaluations.The algorithms all have been implemented and tested. Preliminary numericalresults are very promising. The number of iterations and function evaluations required to converge to a solution are, on average, roughly the same as for a widely available state-of-the-art feasible SQP implementation, whereas the amount of computation required per iteration is much less. The ability of the algorithms to effectively solve real problems from engineering design is demonstrated by considering signal set design problems for optimal detection in the presence of non-Gaussian noise

A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven to converge to a locally optimal solution. Assuming that the first convex problem in the sequence is feasible, these properties are obtained by convexifying the non-convex cost and inequality constraints with inner-convex approximations. Additionally, a computationally efficient method is introduced to obtain inner-convex approximations based on Taylor series expansions. These Taylor-based inner-convex approximations provide the overall algorithm with a quadratic rate of convergence. The proposed method is capable of solving problems of practical interest in real-time. This is illustrated with a numerical simulation of an aerial vehicle trajectory optimization problem on commercial-of-the-shelf embedded computers

Fusion of Head and Full-Body Detectors for Multi-Object Tracking

In order to track all persons in a scene, the tracking-by-detection paradigm has proven to be a very effective approach. Yet, relying solely on a single detector is also a major limitation, as useful image information might be ignored. Consequently, this work demonstrates how to fuse two detectors into a tracking system. To obtain the trajectories, we propose to formulate tracking as a weighted graph labeling problem, resulting in a binary quadratic program. As such problems are NP-hard, the solution can only be approximated. Based on the Frank-Wolfe algorithm, we present a new solver that is crucial to handle such difficult problems. Evaluation on pedestrian tracking is provided for multiple scenarios, showing superior results over single detector tracking and standard QP-solvers. Finally, our tracker ranks 2nd on the MOT16 benchmark and 1st on the new MOT17 benchmark, outperforming over 90 trackers.Comment: 10 pages, 4 figures; Winner of the MOT17 challenge; CVPRW 201

Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems