In this paper we provide a theoretical and numerical comparison of convergence rates forward-backward, Douglas-Rachford, Peaceman-Rachford algorithms for minimizing the sum convex proper lower semicontinuous function strongly differentiable with Lipschitz continuous gradient. Our results extend made in [1], when both functions are smooth, to context where only one is assumed differentiable. Opt...

EQUALITY CONSTRAINED OPTIMIZATION Masao Fukushima Kyoto University Hisashi Mine Kansai University Eiki Yamakawa Kyoto University (Received November 12, 1984: Revised June 12, 1985) This paper is concerned with a differentiable exact penalty function derived by modifying the Wolfe dual of an equality constrained problem. It may be considered that this penalty function belongs to a class of gener...

Signal to Noise Ratio (SNR) is an important index for wireless communications. There are many methods for increasing SNR. In CDMA systems, spreading sequences are used. To increase SNR, we have to improve spreading sequences. In classical approaches, the expression of SNR is not differentiable in terms of the parameter of the spreading sequences even in no fading situations. Thus, we express it...

Developing optimal flocking control procedure is an essential problem in mobile sensor networks (MSNs). Furthermore, finding the parameters such that the sensors can reach to the target in an appropriate time is an important issue. This paper offers an optimization approach based on metaheuristic methods for flocking control in MSNs to follow a target. We develop a non-differentiable optimizati...

An inventory model is formulated with type-2 fuzzy parameters under trade credit policy and solved by using Generalized Hukuhara derivative approach. Representing demand parameter of each expert's opinion is a membership function of type-1 and thus, this membership function again becomes fuzzy. The final opinion of all experts is expressed by a type-2 fuzzy variable. For this present problem, t...

A reformulation of the nonlinear complementarity problem (NCP) as an unconstrained minimization problem is considered. It is shown that any stationary point of the unconstrained objective function is already a solution of NCP if the mapping F involved in NCP is continuously differentiable and monotone. A descent algorithm is described which uses only function values of F. Some numerical results...

We discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the bound is concave. In particular we consider two concrete applications of the method, namely sparse learning and support vector classification. 1 Optimization b...

Invariants that incrementally maintain the value of expressions under assignments to their variables are a natural abstraction to build high-level local search algorithms. But their functionalities are not sufficient to allow arbitrary expressions as constraints or objective functions as in constraint programming. Differentiable invariants bridge this expressiveness gap. A differentiable invari...