Maximization of A convex quadratic function under linear constraints

Maximization of A convex quadratic function under linear constraints

Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints

For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of ε-subdifferentials of convex functions and ε-normal directions, to convex sets. By specializing the problem of maximizing a convex function over a c...

On utility maximization under convex portfolio constraints

Efficient Submodular Function Maximization under Linear Packing Constraints

We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix A ∈ [0, 1]m×n, a vector b ∈ [1,∞)m, and a monotone submodular set function f : 2 → R+. The objective is to find a set S that maximizes f(S) subject to AxS ≤ b. Here, xS stands for the characteristic vector of the set S. A well-studied spec...

On convex quadratic programs with linear complementarity constraints

The paper shows that the global resolution of a general convex quadratic program with complementarity constraints (QPCC), possibly infeasible or unbounded, can be accomplished in finite time. The method constructs a minmax mixed integer formulation by introducing finitely many binary variables, one for each complementarity constraint. Based on the primal-dual relationship of a pair of convex qu...