Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to handle inconsistent linearizations. Numerical tests are performed to investigate the behaviour of the class of algorithms.Comment: 18 pages, 1 figur

Sequential Convex Programming Methods for A Class of Structured Nonlinear Programming

In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming problem exactly or inexactly. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the methods is a KKT point of the SNLP problems. In addition, we propose a variant of the exact SCP method for SNLP in which nonmonotone scheme and "local" Lipschitz constants of the associated functions are used. And a similar convergence result as mentioned above is established.Comment: This paper has been withdrawn by the author due to major revision and correction

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

Globally Optimal Energy-Efficient Power Control and Receiver Design in Wireless Networks

The characterization of the global maximum of energy efficiency (EE) problems in wireless networks is a challenging problem due to the non-convex nature of investigated problems in interference channels. The aim of this work is to develop a new and general framework to achieve globally optimal solutions. First, the hidden monotonic structure of the most common EE maximization problems is exploited jointly with fractional programming theory to obtain globally optimal solutions with exponential complexity in the number of network links. To overcome this issue, we also propose a framework to compute suboptimal power control strategies characterized by affordable complexity. This is achieved by merging fractional programming and sequential optimization. The proposed monotonic framework is used to shed light on the ultimate performance of wireless networks in terms of EE and also to benchmark the performance of the lower-complexity framework based on sequential programming. Numerical evidence is provided to show that the sequential fractional programming framework achieves global optimality in several practical communication scenarios.Comment: Accepted for publication in the IEEE Transactions on Signal Processin

Decentralized Model Predictive Control of Swarms of Spacecraft Using Sequential Convex Programming

This paper presents a decentralized, model predictive control algorithm for the reconfiguration of swarms of spacecraft composed of hundreds to thousands of agents with limited capabilities. In our prior work, sequential convex programming has been used to determine collision-free, fuel-efficient trajectories for the reconfiguration of spacecraft swarms. This paper uses a model predictive control approach to implement the sequential convex programming algorithm in real-time. 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

NUM-Based Rate Allocation for Streaming Traffic via Sequential Convex Programming

In recent years, there has been an increasing demand for ubiquitous streaming like applications in data networks. In this paper, we concentrate on NUM-based rate allocation for streaming applications with the so-called S-curve utility functions. Due to non-concavity of such utility functions, the underlying NUM problem would be non-convex for which dual methods might become quite useless. To tackle the non-convex problem, using elementary techniques we make the utility of the network concave, however this results in reverse-convex constraints which make the problem non-convex. To deal with such a transformed NUM, we leverage Sequential Convex Programming (SCP) approach to approximate the non-convex problem by a series of convex ones. Based on this approach, we propose a distributed rate allocation algorithm and demonstrate that under mild conditions, it converges to a locally optimal solution of the original NUM. Numerical results validate the effectiveness, in terms of tractable convergence of the proposed rate allocation algorithm.Comment: 6 pages, conference submissio