Outer Approximation Method for the Unit Commitment Problem with Wind Curtailment and Pollutant Emission

This paper considers the fast and effective solving method for the unit commitment (UC) problem with wind curtailment and pollutant emission in power systems. Firstly, a suitable mixed-integer quadratic programming (MIQP) model of the corresponding UC problem is presented by some linearization techniques, which is difficult to solve directly. Then, the MIQP model is solved by the outer approximation method (OAM), which decomposes the MIQP into a mixed-integer linear programming (MILP) master problem and a nonlinear programming (NLP) subproblem for alternate iterative solving. Finally, simulation results for six systems with up to 100 thermal units and one wind unit in 24 periods are presented, which show the practicality of MIQP model and the effectiveness of OAM.

Partially distributed outer approximation

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

Chance constrained optimization of elliptic PDE systems with a smoothing convex approximation

In this paper, we consider chance constrained optimization of elliptic partial differential equation (CCPDE) systems with random parameters and constrained state variables. We demonstrate that, under standard assumptions, CCPDE is a convex optimization problem. Since chance constrained optimization problems are generally nonsmooth and difficult to solve directly, we propose a smoothing inner-outer approximation method to generate a sequence of smooth approximate problems for the CCPDE. Thus, the optimal solution of the convex CCPDE is approximable through optimal solutions of the inner-outer approximation problems. A numerical example demonstrates the viability of the proposed approach.