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maximizing sum over feasible set of vectors

Let [5] be the set of the first 5 positive integers. We let α_=(αA)A,A[5] consist of a vector with 31 real entries, where each αA is associated with a subset A[5].

Define OBJ(α_)=A[5],AαAlog(|A|), v(α_)=A[5],AαA, and E(α_)=A,B:ABαAαB, where the sum for E(α_) is taken over all unordered pairs of disjoint nonempty sets A and B.

Also define FEAS(1/4) to be the set of all such vectors α_ with nonnegative real entries such that v(α_)=1 and E(α_)1/4.

I want to learn how to program the following optimization problem: OPT(1/4):=maxα_FEAS(1/4)OBJ(α_)

I was told that I can do this in SageMath. I have some basic knowledge of how to use Sage. How could I create the set FEAS(1/4)? I think that from there I may be able to figure out how to maximize OBJ(α_) over this set.

maximizing sum over feasible set of vectors

Let [5] be the set of the first 5 positive integers. We let α_=(αA)A,A[5] consist of a vector with 31 real entries, where each αA is associated with a subset A[5].

Define OBJ(α_)=A[5],AαAlog(|A|), v(α_)=A[5],AαA, and E(α_)=A,B:ABαAαB, where the sum for E(α_) is taken over all unordered pairs of disjoint nonempty sets A and B.B, where A,B[5].

Also define FEAS(1/4) to be the set of all such vectors α_ with nonnegative real entries such that v(α_)=1 and E(α_)1/4.

I want to learn how to program the following optimization problem: OPT(1/4):=maxα_FEAS(1/4)OBJ(α_)

I was told that I can do this in SageMath. I have some basic knowledge of how to use Sage. How could I create the set FEAS(1/4)? I think that from there I may be able to figure out how to maximize OBJ(α_) over this set.

maximizing sum over feasible set of vectors

Let [5] be the set of the first 5 positive integers. We let α_=(αA)A,A[5] consist of a vector with 31 real entries, where each αA is associated with a subset A[5].

Define OBJ(α_)=A[5],AαAlog(|A|), v(α_)=A[5],AαA, and E(α_)=A,B:ABαAαB, where the sum for E(α_) is taken over all unordered pairs of disjoint nonempty sets A and B, where A,B[5].

Also define FEAS(1/4) to be the set of all such vectors α_ with nonnegative real entries such that v(α_)=1 and E(α_)1/4.

I want to learn how to program the following optimization problem: OPT(1/4):=maxα_FEAS(1/4)OBJ(α_)

I was told that I can do this in SageMath. I have some basic knowledge of how to use Sage. How could I create the set FEAS(1/4)? I think that from there I may be able to figure out how to maximize OBJ(α_) over this set.