The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-d...

This paper presents a new practical approach to complex quadratic programming which solves the broad class of complex approximation problems employing finitization of semi-infinite formulations. The approximation problem may be general with arbitrarily complex basis functions. By using a new technique, the associated semi-infinite quadratic programming problem can be solved taking advantage of ...

We propose an algorithm to locate an object with unknown coordinates based on the positive semi-definite programming in the wireless sensor networks, assuming that the squared error of the measured distance follows Gaussian distribution. We first obtain the estimator of the object location; then transform the non-convex problem to convex one by the positive semi-definite relaxation; and finally...

The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program -minimize a convex function subject to inequality constraints on other convex functions. The present approach uses the support planes of the constraint region to transform the convex program into an equivalent linear program. Then the d...

In this paper, we introduce three new types of generalized convex functions, called semi E-pseudoinvex, strictly semi Epseudoinvex and semi E-quasiinvex functions. Then some of their basic properties are studied, We used directional derivative and obtain the new results in this class of functions. As applications of our results, we obtain optimal solutions for multiobjective programming. AMS Su...

The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. We first propose a quite accurate approximation of the numb...