update

src/lib/lbfgs.c

@@ -148,6 +148,20 @@ static int line_search_backtracking(
     const lbfgs_parameter_t *param
     );
 
+static int line_search_backtracking_quad(
+    int n,
+    lbfgsfloatval_t *x,
+    lbfgsfloatval_t *f,
+    lbfgsfloatval_t *g,
+    lbfgsfloatval_t *s,
+    lbfgsfloatval_t *stp,
+    const lbfgsfloatval_t* xp,
+    const lbfgsfloatval_t* gp,
+    lbfgsfloatval_t *wa,
+    callback_data_t *cd,
+    const lbfgs_parameter_t *param
+    );
+
 static int line_search_backtracking_owlqn(
     int n,
     lbfgsfloatval_t *x,
@@ -370,6 +384,11 @@ int lbfgs(
         case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE:
             linesearch = line_search_backtracking;
             break;
+        case LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD:
+        //case LBFGS_LINESEARCH_BACKTRACKING_WOLFE_QUAD:
+        //case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE_QUAD:
+            linesearch = line_search_backtracking_quad;
+            break;
         default:
             return LBFGSERR_INVALID_LINESEARCH;
         }
@@ -945,6 +964,91 @@ static int line_search_backtracking(
     }
 }
 
+static int line_search_backtracking_quad(
+    int n,
+    lbfgsfloatval_t *x,
+    lbfgsfloatval_t *f,
+    lbfgsfloatval_t *g,
+    lbfgsfloatval_t *s,
+    lbfgsfloatval_t *stp,
+    const lbfgsfloatval_t* xp,
+    const lbfgsfloatval_t* gp,
+    lbfgsfloatval_t *wp,
+    callback_data_t *cd,
+    const lbfgs_parameter_t *param
+    )
+{
+    int count = 0;
+    lbfgsfloatval_t dg, stp2;
+    lbfgsfloatval_t finit, dginit = 0., dgtest;
+    const lbfgsfloatval_t dec = 0.5;
+
+    /* Check the input parameters for errors. */
+    if (*stp <= 0.) {
+        return LBFGSERR_INVALIDPARAMETERS;
+    }
+
+    /* Compute the initial gradient in the search direction. */
+    vecdot(&dginit, g, s, n); //计算点积 g为梯度方向 s为下降方向
+
+    /* Make sure that s points to a descent direction. */
+    if (0 < dginit) {
+        return LBFGSERR_INCREASEGRADIENT;
+    }
+
+    /* The initial value of the objective function. */
+    finit = *f;
+    dgtest = param->ftol * dginit; // ftol 大概为 function tolerance
+
+    for (;;) {
+        veccpy(x, xp, n);
+        vecadd(x, s, *stp, n); // vecadd x += (*stp)*s
+
+        /* Evaluate the function and gradient values. */
+        // 这里我们发现的cd的用法，即传递函数指针
+        *f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);
+
+        ++count;
+
+        // 充分下降条件
+        if (*f > finit + *stp * dgtest) {
+            stp2 = 0.5*dginit*(*stp)*(*stp)/(finit - (*f) + dginit*(*stp));
+            if (stp2 < 0) {
+                (*stp) *= dec;
+            }
+            else {
+                (*stp) = stp2;
+            }
+            
+        } else {
+            // 充分下降条件满足并搜索方法为backtracking，搜索条件为Armijo，则可以退出了。否则更新步长，继续搜索。
+            /* The sufficient decrease condition (Armijo condition). */
+            if (param->linesearch == LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD) {
+                /* Exit with the Armijo condition. */
+                return count;
+	        }
+
+        }
+
+        // 以下情况返回的步长不能保证满足搜索条件
+        if (*stp < param->min_step) {
+            /* The step is the minimum value. */
+            // 退出 此时步长小于最小步长
+            return LBFGSERR_MINIMUMSTEP;
+        }
+        if (*stp > param->max_step) {
+            /* The step is the maximum value. */
+            // 退出 此时步长大于最大步长
+            return LBFGSERR_MAXIMUMSTEP;
+        }
+        if (param->max_linesearch <= count) {
+            /* Maximum number of iteration. */
+            // 退出 线性搜索次数超过了最大限制
+            return LBFGSERR_MAXIMUMLINESEARCH;
+        }
+    }
+}
+
 // 还是反向搜索 只是添加了L1模方向
 static int line_search_backtracking_owlqn(
     int n,

src/lib/lbfgs.h

@@ -197,6 +197,14 @@ enum {
      *  a is the step length.
      */
     LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE = 3,
+
+    LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD = 4,
+
+    //LBFGS_LINESEARCH_BACKTRACKING_QUAD = 5,
+
+    //LBFGS_LINESEARCH_BACKTRACKING_WOLFE_QUAD = 5,
+
+    //LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE_QUAD = 6,
 };
 
 // L-BFGS参数类型。参数很多，简要说明如下：

src/sample/sample2.cpp

@@ -39,10 +39,16 @@ public:
             Start the L-BFGS optimization; this will invoke the callback functions
             evaluate() and progress() when necessary.
          */
-        int ret = lbfgs(N, m_x, &fx, _evaluate, _progress, this, NULL, NULL);
+        lbfgs_parameter_t self_para;
+        lbfgs_parameter_init(&self_para);
+        self_para.epsilon = 1e-7;
+        //self_para.linesearch = LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD;
+        //self_para.ftol = 1e-3;
+
+        int ret = lbfgs(N, m_x, &fx, _evaluate, _progress, this, &self_para, NULL);
 
         /* Report the result. */
-        printf("L-BFGS optimization terminated with status code = %d\n", ret);
+        printf("L-BFGS optimization terminated with status: %s\n", lbfgs_strerror(ret));
         printf("  fx = %f, x[0] = %f, x[1] = %f\n", fx, m_x[0], m_x[1]);
         
         return ret;
@@ -111,7 +117,7 @@ protected:
     {
         printf("Iteration %d:\n", k);
         printf("  fx = %f, x[0] = %f, x[1] = %f\n", fx, x[0], x[1]);
-        printf("  xnorm = %f, gnorm = %f, step = %f\n", xnorm, gnorm, step);
+        printf("  xnorm = %f, gnorm = %f, step = %f, convergence = %e\n", xnorm, gnorm, step, gnorm/xnorm);
         printf("\n");
         return 0;
     }

src/sample/sample4.cpp

@@ -186,6 +186,8 @@ int TEST_FUNC::Routine()
 	lbfgs_parameter_t self_para;
 	lbfgs_parameter_init(&self_para);
 	self_para.epsilon = 1e-7;
+    self_para.linesearch = LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD;
+    self_para.ftol = 1e-3;
 
 	int ret = lbfgs(N, x, &fx, _Func, _Progress, this, &self_para, _Precondition);