We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qu...

in this paper, an efficient method for solving optimal control problemsof the linear differential systems with inequality constraint is proposed. by usingnew adjustment of hat basis functions and their operational matrices of integration,optimal control problem is reduced to an optimization problem. also, the erroranalysis of the proposed method is investigated and it is proved that the order o...

where mj > 0, dj > 0, j ∈ J, x = (xj)j∈J, and J def = {1, . . . , n}. Denote this problem by (Q≤) in the first case (problem (1.1)–(1.3) with inequality “≤” constraint (1.2)), by (Q) in the second case (problem (1.1)–(1.3) with equality constraint (1.2)), and by (Q≥) in the third case (problem (1.1)–(1.3) with inequality “≥” constraint (1.2)). Denote by X≤, X, X≥ the feasible set (1.2)–(1.3) in...

In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is rstly converted into an optimization problem with a single...

An important class of optimization problems in control and signal processing involves the constraint that a Popov function is nonnegative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finitedimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality r...

An important class of optimization problems in control and signal processing involves the constraint that a Popov function is nonnegative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finitedimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality r...

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...

We consider a chance constraint Prob{ξ : A(x, ξ) ∈ K} ≥ 1 − 2 (x is the decision vector, ξ is a random perturbation, K is a closed convex cone, and A(·, ·) is bilinear). While important for many applications in Optimization and Control, chance constraints typically are “computationally intractable”, which makes it necessary to look for their tractable approximations. We present these approximat...

• An inequality constrained optimization problem is an optimization problem in which the constraint set D can be represented as D = U ∩ {x ∈ R | h(x) ≥ 0}, where h : R → R. We refer to the functions h = (h1, . . . , hl) as inequality constraints. • An optimization problem with mixed constraints is an optimization problem in which the constraint set D can be represented as D = U ∩ {x ∈ R | g(x) ...