We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An ...

Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of Lagrange multipliers in network resource allocation, a novel learn-andadapt stochastic dual gradient (LA-SDG) method is developed in this paper to learn the s...

In this paper, we consider the problem of minimum-norm control of the double integrator with bilateral inequality constraints for the output. We approximate the constraints by piecewise linear functions and prove that the Lagrange multipliers associated with the state constraints of the approximating problem are discrete measures, concentrated in at most two points in every interval of discreti...

In this paper, a sub-optimal boundary control strategy for free problem is investigated. The model described by non-smooth convection-diffusion equation. addressed an instantaneous based on the characteristics method. resulting time independent problems are formulated as function space optimization with complementarity constraints. At each step, existence of optimal solution proved and first-or...

The Variational Iteration Method (VIM) is an iterative method that approximates solutions of differential equations. The method is a modification of the so-called general Lagrange multipliers [2]. The method is based on the idea of constructing a correction functional that uses a Lagrange multiplier. In this study, we analyse some basic properties of the Lagrange multiplier; and using these, we...

In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses rest...

Recently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the output and input probability density function (pdf) of the deconvolutional process were approximated with the maximum entropy density approximation tech...

In the rst part of this article, we have shown how time-dependent optimal control for partial di erential equations can be realized in a modern high-level modeling and simulation package. In this second part we extend our approach to (state) constrained problems. Pure state constraints in a function space setting lead to non-regular Lagrange multipliers (if they exist), i.e. the Lagrange multip...

We have proposed a neural network called the Lagrange programming neural network with polarized high-order connections (LPPH) for solving the satisfiability problem (SAT) of propositional calculus. The LPPH has gradient descent dynamics for variables and gradient ascent dynamics for Lagrange multipliers, which represent the weights of the clauses of the SAT. Each weight wr increases according t...

In recent years, parallel computers have changed techniques to solve problems in various kinds of fields. In parallel computers of distributed memory type, data can be shared by communication procedures called message-passing, whose speed is slower than that of computations in a processor. From a practical point of view, it is important to reduce the amount of message-passing. Domain-decomposit...