optimize: make function converger an interface

Fixes #488.
Updates #677.

optimize/cmaes_test.go

@@ -42,6 +42,7 @@ func cmaTestCases() []cmaTestCase {
 			},
 			settings: &Settings{
 				FunctionThreshold: 0.01,
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != FunctionThreshold {
@@ -63,6 +64,7 @@ func cmaTestCases() []cmaTestCase {
 			method: &CmaEsChol{},
 			settings: &Settings{
 				FunctionThreshold: math.Inf(-1),
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != MethodConverge {
@@ -88,6 +90,7 @@ func cmaTestCases() []cmaTestCase {
 			settings: &Settings{
 				FunctionThreshold: math.Inf(-1),
 				MajorIterations:   10,
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != IterationLimit {
@@ -117,6 +120,7 @@ func cmaTestCases() []cmaTestCase {
 			settings: &Settings{
 				FunctionThreshold: math.Inf(-1),
 				FuncEvaluations:   250, // Somewhere in the middle of an iteration.
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != FunctionEvaluationLimit {
@@ -147,6 +151,7 @@ func cmaTestCases() []cmaTestCase {
 			},
 			settings: &Settings{
 				FunctionThreshold: math.Inf(-1),
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != MethodConverge {
@@ -172,6 +177,7 @@ func cmaTestCases() []cmaTestCase {
 			},
 			settings: &Settings{
 				FunctionThreshold: math.Inf(-1),
+				Converger:         NeverTerminate{},
 			},
 			good: func(result *Result, err error, concurrent int) error {
 				if result.Status != MethodConverge {

optimize/functionconvergence.go

@@ -4,10 +4,38 @@
 
 package optimize
 
-import "math"
+import (
+	"math"
+)
 
-// FunctionConverge tests for the convergence of function values. See comment
-// in Settings.
+// Converger returns the convergence of the optimization based on
+// locations found during optimization. Converger must not modify the value of
+// the provided Location in any of the methods.
+type Converger interface {
+	Init(dim int)
+	Converged(loc *Location) Status
+}
+
+// NeverTerminate implements Converger, always reporting NotTerminated.
+type NeverTerminate struct{}
+
+func (NeverTerminate) Init(dim int) {}
+
+func (NeverTerminate) Converged(loc *Location) Status {
+	return NotTerminated
+}
+
+// FunctionConverge tests for insufficient improvement in the optimum value
+// over the last iterations. A FunctionConvergence status is returned if
+// there is no significant decrease for FunctionConverge.Iterations. A
+// significant decrease is considered if
+//   f < f_best
+// and
+//  f_best - f > FunctionConverge.Relative * maxabs(f, f_best) + FunctionConverge.Absolute
+// If the decrease is significant, then the iteration counter is reset and
+// f_best is updated.
+//
+// If FunctionConverge.Iterations == 0, it has no effect.
 type FunctionConverge struct {
 	Absolute   float64
 	Relative   float64
@@ -18,13 +46,14 @@ type FunctionConverge struct {
 	iter  int
 }
 
-func (fc *FunctionConverge) Init() {
+func (fc *FunctionConverge) Init(dim int) {
 	fc.first = true
 	fc.best = 0
 	fc.iter = 0
 }
 
-func (fc *FunctionConverge) FunctionConverged(f float64) Status {
+func (fc *FunctionConverge) Converged(l *Location) Status {
+	f := l.F
 	if fc.first {
 		fc.best = f
 		fc.first = false

optimize/global.go

@@ -12,7 +12,7 @@ import (
 func DefaultSettingsGlobal() *Settings {
 	return &Settings{
 		FunctionThreshold: math.Inf(-1),
-		FunctionConverge: &FunctionConverge{
+		Converger: &FunctionConverge{
 			Absolute:   1e-10,
 			Iterations: 100,
 		},

optimize/listsearch_test.go

@@ -48,7 +48,9 @@ func TestListSearch(t *testing.T) {
 		method := &ListSearch{
 			Locs: locs,
 		}
-		settings := &Settings{}
+		settings := &Settings{
+			Converger: NeverTerminate{},
+		}
 		initX := make([]float64, c)
 		result, err := Minimize(p, initX, settings, method)
 		if err != nil {

optimize/local_example_test.go

@@ -22,7 +22,7 @@ func ExampleMinimize() {
 	settings := optimize.DefaultSettingsLocal()
 	settings.Recorder = nil
 	settings.GradientThreshold = 1e-12
-	settings.FunctionConverge = nil
+	settings.Converger = optimize.NeverTerminate{}
 
 	result, err := optimize.Minimize(p, x, settings, &optimize.BFGS{})
 	if err != nil {

optimize/minimize.go

@@ -143,12 +143,17 @@ func Minimize(p Problem, initX []float64, settings *Settings, method Method) (*R
 	optLoc := newLocation(dim, method)
 	optLoc.F = math.Inf(1)
 
-	if settings.FunctionConverge != nil {
-		settings.FunctionConverge.Init()
-	}
-
 	initOp, initLoc := getInitLocation(dim, initX, settings.InitValues, method)
 
+	converger := settings.Converger
+	if converger == nil {
+		converger = &FunctionConverge{
+			Absolute:   1e-10,
+			Iterations: 20,
+		}
+	}
+	converger.Init(dim)
+
 	stats.Runtime = time.Since(startTime)
 
 	// Send initial location to Recorder
@@ -161,7 +166,7 @@ func Minimize(p Problem, initX []float64, settings *Settings, method Method) (*R
 
 	// Run optimization
 	var status Status
-	status, err = minimize(&p, method, settings, stats, initOp, initLoc, optLoc, startTime)
+	status, err = minimize(&p, method, settings, converger, stats, initOp, initLoc, optLoc, startTime)
 
 	// Cleanup and collect results
 	if settings.Recorder != nil && err == nil {
@@ -184,7 +189,7 @@ func getDefaultMethod(p *Problem) Method {
 
 // minimize performs an optimization. minimize updates the settings and optLoc,
 // and returns the final Status and error.
-func minimize(prob *Problem, method Method, settings *Settings, stats *Stats, initOp Operation, initLoc, optLoc *Location, startTime time.Time) (Status, error) {
+func minimize(prob *Problem, method Method, settings *Settings, converger Converger, stats *Stats, initOp Operation, initLoc, optLoc *Location, startTime time.Time) (Status, error) {
 	dim := len(optLoc.X)
 	nTasks := settings.Concurrent
 	if nTasks == 0 {
@@ -317,7 +322,7 @@ func minimize(prob *Problem, method Method, settings *Settings, stats *Stats, in
 		case NoOperation:
 			// Just send the task back.
 		case MajorIteration:
-			status = performMajorIteration(optLoc, task.Location, stats, startTime, settings)
+			status = performMajorIteration(optLoc, task.Location, stats, converger, startTime, settings)
 		case MethodDone:
 			methodDone = true
 			status = MethodConverge
@@ -504,7 +509,7 @@ func updateEvaluationStats(stats *Stats, op Operation) {
 // the convergence criteria given by settings. Otherwise a corresponding status is
 // returned.
 // Unlike checkLimits, checkConvergence is called only at MajorIterations.
-func checkLocationConvergence(loc *Location, settings *Settings) Status {
+func checkLocationConvergence(loc *Location, settings *Settings, converger Converger) Status {
 	if math.IsInf(loc.F, -1) {
 		return FunctionNegativeInfinity
 	}
@@ -517,10 +522,7 @@ func checkLocationConvergence(loc *Location, settings *Settings) Status {
 	if loc.F < settings.FunctionThreshold {
 		return FunctionThreshold
 	}
-	if settings.FunctionConverge != nil {
-		return settings.FunctionConverge.FunctionConverged(loc.F)
-	}
-	return NotTerminated
+	return converger.Converged(loc)
 }
 
 // checkEvaluationLimits checks the optimization limits after an evaluation
@@ -559,11 +561,11 @@ func checkIterationLimits(loc *Location, stats *Stats, settings *Settings) Statu
 // performMajorIteration does all of the steps needed to perform a MajorIteration.
 // It increments the iteration count, updates the optimal location, and checks
 // the necessary convergence criteria.
-func performMajorIteration(optLoc, loc *Location, stats *Stats, startTime time.Time, settings *Settings) Status {
+func performMajorIteration(optLoc, loc *Location, stats *Stats, converger Converger, startTime time.Time, settings *Settings) Status {
 	copyLocation(optLoc, loc)
 	stats.MajorIterations++
 	stats.Runtime = time.Since(startTime)
-	status := checkLocationConvergence(optLoc, settings)
+	status := checkLocationConvergence(optLoc, settings, converger)
 	if status != NotTerminated {
 		return status
 	}

optimize/types.go

@@ -185,18 +185,18 @@ type Settings struct {
 	// The default value is 1e-6.
 	GradientThreshold float64
 
-	// FunctionConverge tests that the function value decreases by a
-	// significant amount over the specified number of iterations.
+	// Converger checks if the optimization has converged based on the (history
+	// of) locations found during the optimizaiton. Minimize will pass the
+	// Location at every MajorIteration to the Converger.
 	//
-	// If f < f_best and
-	//  f_best - f > FunctionConverge.Relative * maxabs(f, f_best) + FunctionConverge.Absolute
-	// then a significant decrease has occurred, and f_best is updated.
-	//
-	// If there is no significant decrease for FunctionConverge.Iterations
-	// major iterations, FunctionConvergence status is returned.
-	//
-	// If this is nil or if FunctionConverge.Iterations == 0, it has no effect.
-	FunctionConverge *FunctionConverge
+	// If the Converger is nil, a default value of
+	//  FunctionConverge {
+	//		Absolute: 1e-10,
+	//		Iterations: 100,
+	//  }
+	// will be used. NeverTerminated can be used to always return a
+	// NotTerminated status.
+	Converger Converger
 
 	// MajorIterations is the maximum number of iterations allowed.
 	// IterationLimit status is returned if the number of major iterations
@@ -245,7 +245,7 @@ func DefaultSettingsLocal() *Settings {
 	return &Settings{
 		GradientThreshold: defaultGradientAbsTol,
 		FunctionThreshold: math.Inf(-1),
-		FunctionConverge: &FunctionConverge{
+		Converger: &FunctionConverge{
 			Absolute:   1e-10,
 			Iterations: 20,
 		},

optimize/unconstrained_test.go

@@ -1164,16 +1164,18 @@ func testLocal(t *testing.T, tests []unconstrainedTest, method Method) {
 		settings.Recorder = nil
 		if method != nil && method.Needs().Gradient {
 			// Turn off function convergence checks for gradient-based methods.
-			settings.FunctionConverge = nil
+			settings.Converger = NeverTerminate{}
 		} else {
 			if test.fIter == 0 {
 				test.fIter = 20
 			}
-			settings.FunctionConverge.Iterations = test.fIter
+			c := settings.Converger.(*FunctionConverge)
+			c.Iterations = test.fIter
 			if test.fAbsTol == 0 {
 				test.fAbsTol = 1e-12
 			}
-			settings.FunctionConverge.Absolute = test.fAbsTol
+			c.Absolute = test.fAbsTol
+			settings.Converger = c
 		}
 		if test.gradTol == 0 {
 			test.gradTol = 1e-12