Dual characterizations of the containment of a convex set with quasiconvex inequality constraints are investigated. A new Lagrange-type duality and a new closed cone constraint qualification are described, and it is shown that this constraint qualification is the weakest constraint qualification for the duality.

Many type based program analyses with subtyping, such as ow analysis, are based on inequality constraints over a lattice. When inequality constraints are combined with polymorphism it is often hard to scale the analysis up to large programs. A major source of ineeciency in conventional implementations stems from computing substitution instances of constraints. In this paper we extend the constr...

We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an O(log n log r)-competitive algorithm (where r is...

A surrogate constraint is an inequality implied by the constraints of an integ~r program, and designed to capture useful information that cannot be extra~ted from the parent constraints individually but is nevertheless a consequepce of their conjunction. The use of such constraints as originally propo~ed by the author has recently been extended in an important way by EGON! BALAS and ARTHUR GEOF...

this paper presents a new observer design methodology for a time varying actuator fault estimation. a new linear matrix inequality (lmi) design algorithm is developed to tackle the limitations (e.g. equality constraint and robustness problems) of the well known so called fast adaptive fault estimation observer (fafe). the fafe is capable of estimating a wide range of time-varying actuator fault...

We present and discuss a method to relax sets described by finitely many smooth convex inequality constraints by the level set of a single smooth convex inequality constraint. Based on error bounds and Lipschitz continuity, special attention is paid to the maximal approximation error and a guaranteed safety margin. Our results allow to safely avoid the obstacle by obeying a single smooth constr...

model order reduction is known as the problem of minimizing the -norm of the difference between the transfer function of the original system and the reduced one. in many papers, linear matrix inequality (lmi) approach is utilized to address the minimization problem. this paper deals with defining an extra matrix inequality constraint to guarantee that the minimum phase characteristic of the sys...

Two-step MIR inequalities are valid inequalities derived from a facet of a simple mixedinteger set with three variables and one constraint. In this paper we investigate how to effectively use these inequalities as cutting planes for general mixed-integer problems. We study the separation problem for single constraint sets and show that it can be solved in polynomial time when the resulting ineq...

where f(w) is called the objective function, gi(w) the inequality constraints, and hi(w) the equality constraints. The optimal value f(w∗) of the objective function is called the value of the optimization problem. The feasible region is defined by all w ∈M for which ∀i = 1, . . . , k : gi(w) ≤ 0 ∧ ∀j = 1, . . . ,m : hj(w). If for an inequality constraint gi(w) = 0, then the constraint gi is cal...