We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...

An inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the second part of the celebrated Hermite-Hadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

In the integers and in certain densely ordered rings that are not fields, projections of the solution set of finitely many homogeneous weak linear inequalities may be defined by finitely many congruence inequalities, where a congruence inequality combines a weak inequality with a system of congruences. These results extend well-known facts about systems of weak linear inequalities over ordered ...

An integral inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the first part of the celebrated HermiteHadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

We show that Farkas’ lemma for linear inequality systems, established in 1902, continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming problems which include classes of robust linear programming problems.

Linear equality and inequality systems with fuzzy parameters defined by the extension principle are called possibilistic linear equality and inequality systems. The solution of these systems is defined in the sense of BellmanZadeh [1]. This paper investigate stability and continuity properties of the solution in the above-named systems.

In this paper, we will try to find a new Lyapunov-type inequality for a class of nonlinear systems, special cases of which contain some well-known Hamiltonian system, EmdenFowler, half-linear and linear differential equations of second order. Our result extends the Lyapunov-type inequality given in [X. Wang, Stability criteria for linear periodic Hamiltonian systems, J. Math. Anal. Appl. 367 (2...

This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality LMI form. Based on Lyapunov stability theory and linear matrix inequality LMI formulation, a simple linear feedback co...

An Ostrowski type inequality for general convex functions defined on linear spaces is generalised. Some inequalities which improve the HermiteHadamard type inequality for convex functions defined on linear spaces are derived using the obtained result. The results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi-inner products, ...