In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method.

Adler and Monteiro (1992) developed a parametric analysis approach that is naturally related to the geometry of the linear pro~am. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, we develop an altemative geometric approach for parametric analysis which does not require the strong complementarity condition. This pa...

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong d...

We propose an extension of primal grammars (Hermann & Galbavý 1997). Primal grammars are term grammars with a high expressive power and good computational properties. The extended grammars have exactly the same properties but are more modular, more concise, and easier to use, as shown by some examples. An algorithm transforming any extended primal grammar into an equivalent primal grammar is pr...

Many interior-point methods for linear programming are based on the properties of the logarithmic barrier function. After a preliminary discussion of the convergence of the (primal) projected Newton barrier method, three types of barrier method are analyzed. These methods may be categorized as primal, dual and primal-dual, and may be derived from the application of Newton’s method to different ...

Little is known about the physiological mechanisms subserving the experience of air hunger and the affective control of breathing in humans. Acute hunger for air after inhalation of CO(2) was studied in nine healthy volunteers with positron emission tomography. Subjective breathlessness was manipulated while end-tidal CO(2-) was held constant. Subjects experienced a significantly greater sense ...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

We deal with duality for almost convex finite dimensional optimization problems by means of the classical perturbation approach. To this aim some standard results from the convex analysis are extended to the case of almost convex sets and functions. The duality for some classes of primal-dual problems is derived as a special case of the general approach. The sufficient regularity conditions we ...

The main contribution of this paper is the construction of a strong duality for the varieties generated by a set of subalgebras of a semi-primal algebra. We also obtain an axiomatization of the objects of the dual category and develop some algebraic consequences (description of the dual of the finite structures and algebras, construction of finitely generated free algebras,. . . ). Eventually, ...