MPS reader mishandles OBJSENSE: maximization is solved as minimization and reported with the wrong objective sign

[LucasBoTang]

Summary

The src/mps_parser.c file mishandles the OBJSENSE section in two independent ways. Together, they cause maximization instances to be solved incorrectly and silently (returning OPTIMAL status with no warnings).

Specifically:

1. The OBJSENSE value is dropped, causing the problem to be solved as a minimization (resulting in a wrong optimum).
2. Even if (1) is fixed, the reported objective value retains the wrong sign.

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Bug 1: OBJSENSE MAXIMIZE is swallowed (Wrong Optimum)

Section headers are currently detected by treating any single alphabetic token as a header:

if (n_tokens == 1 && isalpha(tokens[0][0]))
{
    MpsSection next_section = SEC_NONE;
    if (strcmp(tokens[0], "ROWS") == 0) next_section = SEC_ROWS;
    /* ... */
    else if (strcmp(tokens[0], "OBJSENSE") == 0) next_section = SEC_OBJSENSE;
    /* ... */

    current_section = next_section;   /* unconditional */
    if (current_section == SEC_ENDATA) break;
    continue;                          /* line consumed */
}

With the standard two-line form:

OBJSENSE
    MAXIMIZE

The value line MAXIMIZE is parsed as a single alphabetic token. It enters the section header block, matches no keywords (so next_section stays SEC_NONE), unconditionally sets current_section = SEC_NONE, and skips to the next line. The case SEC_OBJSENSE: block that should set is_maximize is never reached. As a result, is_maximize defaults to false, the objective is not negated, and the problem is minimized instead.

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Reproduction

Consider the following problem: maximize x s.t. x <= 5, x >= 0 (True optimum x* = 5, objective 5):

NAME          maxtest
OBJSENSE
    MAXIMIZE
ROWS
 N  obj
 L  c1
COLUMNS
    x         obj                  1.0   c1             1.0
RHS
    rhs       c1                   5.0
BOUNDS
ENDATA

• Expected: OPTIMAL, x ~= 5, Objective = 5
• Actual: OPTIMAL, x ~= 0, Objective = 0 (The problem was treated as a minimization)

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Bug 2: Objective sign is not restored for maximization (Wrong Reported Value)

When is_maximize is successfully parsed, the parser converts max → min by negating the objective:

prob->objective_constant = state.is_maximize ? -state.objective_constant
                                             : state.objective_constant;
/* ... */
if (state.is_maximize)
    for (int i = 0; i < prob->num_variables; ++i)
        prob->objective_vector[i] *= -1.0;

However, is_maximize is strictly a local parser variable—it is not stored on the returned lp_problem_t struct, and nothing ever negates the reported objective back at the end of the solve. Consequently, the solver reports min(-c·x) = -(max value).

If Bug 1 is fixed, running the reproduction above yields the correct x* = 5 but reports an objective of -5 instead of +5 (since cupdlpx.c contains no objective-sense restoration logic).

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Suggested Fixes

1. For Bug 1: Restrict the section header detection so that it does not falsely match single-token values inside the OBJSENSE section, or explicitly check for valid section keywords before overwriting current_section.
2. For Bug 2: Add an is_maximize flag (or an obj_sense variable) to the lp_problem_t struct to store the original problem sense. Use this flag in the solver output step to negate the final objective value back to the correct sign before reporting.