A three-term conjugate gradient method with nonmonotone line search for unconstrained optimization

The technique of nonmontone line search has received much attention in nonlinear optimization. This technique can improve the computational cost of the line search process and increase the rate of convergence of the algorithm. However, the convergence of this line search scheme utilizes some rather restrictive assumption concerning the search directions, which may not hold for most conjugate gradient methods. Thus in this paper, we propose a three-term conjugate gradient method with nonmonotone backtracking line search technique for solving large scale unconstrained optimization problems. Convergence analysis of the proposed method is established under reasonable conditions. Numerical experiments carried out on benchmark test problems has clearly indicated the effectiveness of the developed algorithm in terms of efficiency and robustness

A novel hybrid backtracking search optimization algorithm for continuous function optimization

Stochastic optimization algorithm provides a robust and efficient approach for solving complex real world problems. Backtracking Search Optimization Algorithm (BSA) is a new stochastic evolutionary algorithm and the aim of this paper is to introduce a hybrid approach combining the BSA and Quadratic approximation (QA), called HBSAfor solving unconstrained non-linear, non-differentiable optimization problems. For the validity of the proposed method the results are compared with five state-of-the-art particle swarm optimization (PSO) variant approaches in terms of the numerical result of the solutions. The sensitivity analysis of the BSA control parameter (F) is also performed

A simple uniformly optimal method without line search for convex optimization

Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that line search is superfluous in attaining the optimal rate of convergence for solving a convex optimization problem whose parameters are not given a priori. In particular, we present a novel accelerated gradient descent type algorithm called auto-conditioned fast gradient method (AC-FGM) that can achieve an optimal $\mathcal{O}(1/k^2)$ rate of convergence for smooth convex optimization without requiring the estimate of a global Lipschitz constant or the employment of line search procedures. We then extend AC-FGM to solve convex optimization problems with H\"{o}lder continuous gradients and show that it automatically achieves the optimal rates of convergence uniformly for all problem classes with the desired accuracy of the solution as the only input. Finally, we report some encouraging numerical results that demonstrate the advantages of AC-FGM over the previously developed parameter-free methods for convex optimization

Minimizing energy below the glass thresholds

Focusing on the optimization version of the random K-satisfiability problem, the MAX-K-SAT problem, we study the performance of the finite energy version of the Survey Propagation (SP) algorithm. We show that a simple (linear time) backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states. A comparative numerical study on one of the most efficient local search procedures is also given.Comment: 12 pages, submitted to Phys. Rev. E, accepted for publicatio

Achievable Sum Rates of Half- and Full-Duplex Bidirectional OFDM Communication Links

While full-duplex (FD) transmission has the potential to double the system capacity, its substantial benefit can be offset by the self-interference (SI) and non-ideality of practical transceivers. In this paper, we investigate the achievable sum rates (ASRs) of half-duplex (HD) and FD transmissions with orthogonal frequency division multiplexing (OFDM), where the non-ideality is taken into consideration. Four transmission strategies are considered, namely HD with uniform power allocation (UPA), HD with non-UPA (NUPA), FD with UPA, and FD with NUPA. For each of the four transmission strategies, an optimization problem is formulated to maximize its ASR, and a (suboptimal/optimal) solution with low complexity is accordingly derived. Performance evaluations and comparisons are conducted for three typical channels, namely symmetric frequency-flat/selective and asymmetric frequency-selective channels. Results show that the proposed solutions for both HD and FD transmissions can achieve near optimal performances. For FD transmissions, the optimal solution can be obtained under typical conditions. In addition, several observations are made on the ASR performances of HD and FD transmissions.Comment: To appear in IEEE TVT. This paper solves the problem of sum achievable rate optimization of bidirectional FD OFDM link, where joint time and power allocation is involve