A mechanism is provided for optimization of mixed-criticality systems. A plurality of strategies is received that are in a fixed order of criticality. For each strategy in the plurality of strategies, a multivariate objective function and a multivariate constraint in a multivariate decision variable is obtained. A number of strategies of the plurality of strategies that are feasible in combination are maximized. A solution that is feasible for the number of strategies that are feasible in combination is generated such that the objective of a least-critical strategy that is feasible in combination with the other strategies in the number of strategies is optimized.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method, in a data processing system, for optimization of mixed-criticality systems, the method comprising: receiving, by a processor in the data processing system, a plurality of strategies, wherein the plurality of strategies are in a fixed order of criticality; for each strategy in the plurality of strategies, obtaining, by the processor, a multivariate objective function and a multivariate constraint in a multivariate decision variable; maximizing, by the processor, a number of strategies of the plurality of strategies that are feasible in combination; and generating, by the processor, a solution that is feasible for the number of strategies that are feasible in combination, such that the objective of a least-critical strategy that is feasible in combination with the other strategies in the number of strategies is optimized. 2. The method of claim 1, wherein maximizing the number of strategies of the plurality of strategies that are feasible in combination solves: P(ξ):maxsminxƒ(s)([x(1) . . . x(s)],ξ,U(s))s.t.x(1)∈X(ξ,U(1)),[x(1)x(2)]∈X(ξ,U(2)); [x(1) . . . x(s)]∈X(ξ,U(s)); 1≦s≦S where P(86 ) denotes the problem solved, ξ is the multivariate random variable, x=[x(1) . . . x(s)] is the decision variable, ƒ(s) is the objective function of the least-critical strategy supported, and X(s) is the feasible region for the strategy s. 3. The method of claim 1, wherein the plurality of strategies are analyzed with respect to a decreasing level of criticality. 4. The method of claim 1, wherein the multivariate constraint is at east one of a multivariate equality constraint or a multivariate inequality constraint. 5. The method of claim 4, wherein the feasible region for the strategy s (X(s)) is defined by the inequalities F(s)(x, ξ, U(s))≦0 and equalities G(s)(x, ξ, U(s))=0, which make use of the uncertainty parameters U(s) for the strategy s. 6. The method of claim 1, wherein for each strategy in the plurality of strategies, the multivariate objective and the multivariate constraint allow for uncertainty therein. 7. The method of claim 1, wherein the uncertainty sets Z(s) given by ξ, U(s) are at least one of interval-based, polyhedral, ellipsoidal, spectrahedral, or a combination thereof and wherein the selected uncertainty sets solves: P′(ξ):maxsminxmax(ξ(s)∈Z(s)(ξ,U(s))ƒ(s)([x(1). . .x(s)],ξ,ζ(s))s.t.x(1)∈X(ξ,ζ(1)),[x(1)x2]∈X(ξ,ζ(2)); [x(1) . . . x(s)]∈X(ξ, ζ(s)); 1≦s≦S. 8. A computer program product comprising a computer readable storage medium having a computer readable program stored therein, wherein the computer readable program, when executed on a computing device, causes the computing device to: receive a plurality of strategies, wherein the plurality of strategies are in a fixed order of criticality; for each strategy in the plurality of strategies, obtain a multivariate objective function and a multivariate constraint in a multivariate decision variable; maximize a number of strategies of the plurality of strategies that are feasible in combination; and generate a solution that is feasible for the number of strategies that are feasible in combination, such that the objective of a least-critical strategy that is feasible in combination with the other strategies in the number of strategies is optimized. 9. The computer program product of claim 8, wherein maximizing the number of strategies of the plurality of strategies that are feasible in combination solves: P(ξ):maxsminxƒ(s)([x(1) . . . x(s)],ξ,U(s))s.t.x(1)∈X(ξ,U(1)),[x(1)x(2)]∈X(ξ,U(2)); [x(1) . . . x(s)]∈X(ξ,U(s)); 1≦s≦S where P(ξ) denotes the problem solved, ξ is the multivariate random variable, x=[x(1) . . . x(s)] is the decision variable, ƒ(s) is the objective function of the least-critical strategy supported, and X(s) is the feasible region for the strategy s. 10. The computer program product of claim 8, wherein the plurality of strategies are analyzed with respect to a decreasing level of criticality. 11. The computer program product of claim 8, wherein the multivariate constraint is at least one of a multivariate equality constraint or a multivariate inequality constraint. 12. The computer program product of claim 11, wherein the feasible region for the strategy s (X(s)) is defined by the inequalities F(s)(x, ξ, U(s))≦0 and equalities G(s)(x, ξ, U(s))=0, which make use of the uncertainty parameters U(s) for the strategy s. 13. The computer program product of claim 8, wherein for each strategy in the plurality of strategies, the multivariate objective and the multivariate constraint allow for uncertainty therein. 14. The computer program product of claim 8, wherein the uncertainty sets Z(s) given by ξ, U(s) are at least one of interval-based, polyhedral, ellipsoidal, spectrahedral, or a combination thereof and wherein the selected uncertainty sets solves: P′(ξ):maxs, minxmax(ζ(s)∈Z(s)(ξ,U(s))ƒ(s)([x(1) . . . x(s)],ξ,ζ(s))s.t.x(1)∈X(ξ,ζ(1)),[x(1)x(2)]∈X(ξ,ζ(2)); [x(1) . . . x(s)]∈X(ξ,ζ(s)); 1≦s≦S. 15. An apparatus comprising: a processor; and a memory coupled to the processor, wherein the memory comprises instructions which, when executed by the processor, cause the processor to: receive a plurality of strategies, wherein the plurality of strategies are in a fixed order of criticality; for each strategy in the plurality of strategies, obtain a multivariate objective function and a multivariate constraint in a multivariate decision variable; maximize a number of strategies of the plurality of strategies that are feasible in combination; and generate a solution that is feasible for the number of strategies that are feasible in combination, such that the Objective of a least-critical strategy that is feasible in combination with the other strategies in the number of strategies is optimized. 16. The apparatus of claim 15, wherein maximizing the number of strategies of the plurality of strategies that are feasible in combination solves: P(ξ):maxsminxƒ(s)([x(1) . . . x(s)],ξ,U(s))s.t.x(1)∈X(ξ,U(1)),[x(1)x(2)]∈X(ξ,U(2)); [x(1) . . . x(s)]∈X(ξ,U(s)); 1≦s≦S where P(ξ) denotes the problem solved, ξ is the multivariate random variable, x=[x(1) . . . x(s)] is the decision variable, ƒ(s) is the objective function of the least-critical strategy supported, and X(s) is the feasible region for the strategy s. 17. The apparatus of claim 15, wherein the plurality of strategies are analyzed with respect to a decreasing level of criticality. 18. The apparatus of claim 15, wherein the multivariate constraint is at least one of a multivariate equality constraint or a multivariate inequality constraint. 19. The apparatus of claim 18, wherein the feasible region for the strategy s (X(s)) is defined by the inequalities F(s)(x, ξ, U(s))≦0 and equalities G(s)(x, ξ,U(s))=0, which make use of the uncertainty parameters U(s) for the strategy s. 20. The apparatus of claim 15, wherein for each strategy in the plurality of strategies, the multivariate objective and the multivariate constraint allow for uncertainty therein.