scalarize: Scalarize multiple objectives into a single objective

In CVXR: Disciplined Convex Optimization

Scalarize multiple objectives into a single objective

Description

Transforms for combining several Minimize/Maximize objectives into one objective for multi-objective optimization. Mirrors CVXPY's cvxpy.transforms.scalarize submodule; access members with $:

Usage

scalarize

Format

A named list of four functions.

Details

• scalarize$weighted_sum(objectives, weights) – weighted sum of objectives.

• scalarize$targets_and_priorities(objectives, priorities, targets, limits = NULL, off_target = 1e-5) – penalize each objective within a [target, limit] range; a negative priority flips the objective sense.

• scalarize$max(objectives, weights) – minimize the largest weighted objective term.

• scalarize$log_sum_exp(objectives, weights, gamma = 1.0) – smooth maximum; gamma -> 0 approaches weighted_sum, gamma -> Inf approaches max.

Value

scalarize itself is a named list of the four functions above. Each function returns a single Objective combining the inputs: max and log_sum_exp always return a Minimize; weighted_sum returns a Minimize when all objectives are Minimize and a Maximize when all are Maximize (mixing the two is an error); targets_and_priorities returns a Minimize or Maximize according to the objective senses (after negative priorities flip them) and the curvature of the combined expression.

Examples

x <- Variable()
objs <- list(Minimize(square(x)), Minimize(square(x - 1)))
obj <- scalarize$weighted_sum(objs, c(1, 1))
psolve(Problem(obj))

CVXR documentation built on Oct. 19, 2026, 5:07 p.m.