We present a price-directive decomposition algorithm to compute an approximate solution of the mixed packing and covering problem; it either finds x ∈ B such that f(x) ≤ c(1 + )a and g(x) ≥ (1 − )b/c or correctly decides that {x ∈ B|f(x) ≤ a, g(x) ≥ b} = ∅. Here f, g are vectors of M ≥ 2 convex and concave functions, respectively, which are nonnegative on the convex compact set ∅ = B ⊆ R ; B ca...

Throughout this paper, we always assume that H is a real Hilbert space with inner product ⟨⋅, ⋅⟩ and norm ‖ ⋅ ‖. Let I denote the identity operator onH. LetH 1 andH 2 be two real Hilbert spaces and letA : H 1 → H 2 be a bounded linear operator. Given closed convex subsets C and Q of H 1 and H 2 , respectively. The split feasibility problem (SFP) (Censor and Elfving 1994 [1]), modeling phase ret...

A novel robust predictive control algorithm for input-saturated uncertain linear discrete-time systems with structured norm-bounded uncertainties is presented. The solution is based on the minimization, at each time instant, of a LMI convex optimization problem obtained by a recursive use of the S-procedure. The general case of N free moves is presented. Stability and feasibility are proved and...

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are nonconvex and involve expectations over random states. The existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic...

recently, gasimov and yenilmez proposed an approach for solving two kinds of fuzzy linear programming (flp) problems. through the approach, each flp problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. then, the crisp problem is solved by the use of the modified subgradient method. in this paper we will have another look at the earlier defuzzifi...

The purpose of this paper is to propose an algorithm for solving the split feasibility problems for total quasi-asymptotically nonexpansive mappings in infinite-dimensional Hilbert spaces. The results presented in the paper not only improve and extend some recent results of Moudafi [Nonlinear Anal. 74:4083-4087, 2011; Inverse Problem 26:055007, 2010], but also improve and extend some recent res...

The so-called nonlinear H 1-control problem in state space is considered with an emphasis on developing machinery with promising computational properties. Both state feedback and output feedback H 1-control problems for a class of nonlinear systems are characterized in terms of continuous positive deenite solutions of algebraic nonlinear matrix inequalities which are convex feasibility problems...

We present a cutting plane algorithm for the feasibility problem that uses a homogenized self-dual approach to regain an approximate center when adding a cut. The algorithm requires a fully polynomial number of Newton steps. One novelty in the analysis of the algorithm is the use of a powerful proximity measure which is widely used in interior point methods but not previously used in the analys...

Let C and Q be nonempty closed convex sets in RN and RM , respectively, and A an M by N real matrix. The split feasibility problem (SFP) is to find x ∈ C with Ax ∈ Q, if such x exist. An iterative method for solving the SFP, called the CQ algorithm, has the following iterative step: x = PC(x + γ A (PQ − I )Ax), where γ ∈ (0, 2/L) with L the largest eigenvalue of the matrix AT A and PC and PQ de...

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am, Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0, 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩m=1GV I(C,Bm, Am) 6= ∅, where GV I(C,Bm, Am) is the solution set of a gener...