Given a function on Rn with many multiple local minima we approximate it from below, via concave minimization, with a piecewise-linear convex function by using sample points from the given function. The piecewise-linear function is then minimized using a single linear program to obtain an approximation to the global minimum of the original function. Successive shrinking of the original search r...

Piecewise linear convex and concave support functions combined with Pijavskii’s method are proposed to be used for solving global optimization problems. Rules for constructing support functions are introduced.

We report tests of CPLP, a piecewise-linear simplex implementation based on the XMP subroutine library. Using test problems of various shapes and origins, we judge CPLP against a comparable linear bounded-variable simplex code that is applied to equivalent linear programs. Our evidence indicates that CPLP is typically 2 to 3 times faster in solving the test problems that are most signiicantly p...

We consider analysis and controller synthesis of piecewise-linear systems. The method is based on constructing quadratic and piecewise-quadratic Lyapunov functions that prove stability and performance for the system. It is shown that proving stability and performance, or designing (state-feedback) controllers, can be cast as convex optimization problems involving linear matrix inequalities that...

We study succinct representations of a convex univariate function φ over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function φ̄ approximating φ when given a black box access to an L-approximation oracle φ̃ of φ (the oracle value is always within a multiplicative factor L from the true value). The piecewise linear function φ̄ has few breakpoints (...

This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming SDP algorithm. The SDP technique is applied to the longterm operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a pi...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...