Summary/Motivation:

Ensure optimality of decision rules (DR) with respect to the PyROS master problem is properly enforced for problems with a nominal objective focus (i.e. objective_focus=ObjectiveType.nominal passed to the PyROS solver).

Let $k \in \{0, 1, \dots\}$ denote the index of the current PyROS iteration. Let $x^\star$ denote the optimal master first-stage variable values for the current iteration. For each $r = 0, 1, \dots, k$, let $z^{r,\star}, y^{r,\star}$ denote the optimal second-stage and state variable values for block $r$ of the master problem of the current iteration. Now let

$$F^{r} = f_1(x^\star) + f_2(x^\star, z^{r,\star}, y^{r,\star}, q^{r}), \qquad r = 0, 1, \dots, k$$

where $f_1$ and $f_2$ are the first-stage and second-stage objective functions, respectively; and $q^0, q^1, \dots, q^k$ are the uncertain parameter realizations of the current master problem. Under a nominal objective focus, the optimality constraint of the DR polishing problem of the current iteration should be

$$F^{0} \geq f_1(x^\star) + f_2(x^\star, z^0, y^0; q^0)$$

in which $z^0, y^0$ are the nominal second-stage and state variables for block 0 of the polishing problem. However, PyROS currently implements

$$F^{k} \geq f_1(x^\star) + f_2(x^\star, z^0, y^0; q^0)$$

which may result in suboptimal polished decision rules.

Changes proposed in this PR:

• Fix DR polishing problem optimality constraint under nominal objective focus

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